MCQ 11 Mark
The ratio between the radius of the base and the height of a cylinder is $2 : 3.$ If its volume is $1617\ cm^3$, the total surface area of the cylinder is:
- A
$308\ cm^2$
- B
$462\ cm^2$
- C
$540\ cm^2$
- ✓
$770\ cm^2$
AnswerCorrect option: D. $770\ cm^2$
$770\ cm^2$
View full question & answer→MCQ 21 Mark
A metallic cylinder of radius $8 \ cm$ and height $2\ cm$ is melted and converted into a right circular cone of height $6\ cm.$ The radius of the base of this cone is:
- A
$4\ cm$
- B
$5\ cm$
- C
$6\ cm$
- ✓
$8\ cm$
AnswerCorrect option: D. $8\ cm$
$8\ cm$
View full question & answer→MCQ 31 Mark
A mason constructs a wall of dimensions $(270\ cm \times 300\ cm \times 350\ cm)$ with bricks, each of size $(22.5\ cm \times 11.25\ cm \times 8.75\ cm)$ and it is assumed that $1818$ space is covered by the mortar. Number of bricks used to construct the wall is:
- A
$11000$
- B
$11100$
- ✓
$11200$
- D
$11300$
AnswerCorrect option: C. $11200$
$11200$
View full question & answer→MCQ 41 Mark
The shape of a glass $($tumbler$)$ is usually in the form of:
View full question & answer→MCQ 51 Mark
How many bricks, each measuring $(25\ cm \times 11.25\ cm \times 6\ cm),$ will be required to construct a wall $(8m \times 6m \times 22.5\ cm)?$
- A
$8000$
- ✓
$6400$
- C
$4800$
- D
$7200$
AnswerCorrect option: B. $6400$
$6400$
View full question & answer→MCQ 61 Mark
Assertion and Reason Type
Each question consists of two statements, namely, Assertion $(A)$ and Reason $(R)$. For selecting the correct answer, use the following code:
|
Assertion $(A)$
|
Reason $(R)$
|
|
The curved surface area of a cone of base radius $3 cm$ and height $4 cm$ is $15\pi\text{cm}^2$
|
Volume of a cone $\pi\text{r}^2\text{h}$
|
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
View full question & answer→MCQ 71 Mark
A circus tent is cylindrical to a height of $4m$ and conical above it. If its diameter is $105m$ and its slant height is $40m$, the total area of canvas required is:
- A
$1760m^2$
- B
$2640m^2$
- C
$3960m^2$
- ✓
$7920m^2$
AnswerCorrect option: D. $7920m^2$
$7920m^2$
View full question & answer→MCQ 81 Mark
If the areas of three adjacent faces of a cuboid are $x, y$ and $z$, respectively, the volume of the cuboid is:
- A
$\text{xyz}$
- B
$2\text{xyz}$
- ✓
$\sqrt{\text{xyz}}$
- D
$\sqrt[3]{\text{xyz}}$
AnswerCorrect option: C. $\sqrt{\text{xyz}}$
$\sqrt{\text{xyz}}$
View full question & answer→MCQ 91 Mark
The total surface area of a hemisphere of radius $7\ cm$ is:
- A
$(588\pi)\text{cm}^2$
- B
$(392\pi)\text{cm}^2$
- ✓
$(147\pi)\text{cm}^2$
- D
$(98\pi)\text{cm}^2$
AnswerCorrect option: C. $(147\pi)\text{cm}^2$
$(147\pi)\text{cm}^2$
View full question & answer→MCQ 101 Mark
A funnel is the combination of:
- A
- B
A cylinder and a hemisphere.
- ✓
A cylinder and frustum of a cone.
- D
AnswerCorrect option: C. A cylinder and frustum of a cone.
A cylinder and frustum of a cone.
View full question & answer→MCQ 111 Mark
A metallic solid sphere of radius $9\ cm$ is melted to form a solid linder of radius $9\ cm.$ The height of the cylin er is:
- ✓
$12\ cm$
- B
$18\ cm$
- C
$36\ cm$
- D
$96\ cm$
AnswerCorrect option: A. $12\ cm$
$12\ cm$
View full question & answer→MCQ 121 Mark
On increasing the radii of the base and the height of a cone by $20\%$, its volume will increase by:
- A
$20\%$
- B
$40\%$
- C
$60\%$
- ✓
$72.8\%$
AnswerCorrect option: D. $72.8\%$
$72.8\%$
View full question & answer→MCQ 131 Mark
The radii of the circular ends of a bucket of height $40\ cm$ are $24\ cm$ and $15\ cm.$ The slant height $($in $cm)$ of the bucket is:
View full question & answer→MCQ 141 Mark
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2\ cm$ and height 1$6\ cm.$ The diameter of each sphere is:
- ✓
$2\ cm$
- B
$3\ cm$
- C
$4\ cm$
- D
$6\ cm$
AnswerCorrect option: A. $2\ cm$
$2\ cm$
View full question & answer→MCQ 151 Mark
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
- A
$1 : 2$
- B
$2 : 1$
- ✓
$1 : 4$
- D
$4 : 1$
AnswerCorrect option: C. $1 : 4$
$1 : 4$
View full question & answer→MCQ 161 Mark
A cylindrical pencil sharpened at one end is a combination of:
- ✓
- B
A cylinder and frustum of a cone.
- C
A cylinder and a hemisphere.
- D
View full question & answer→MCQ 171 Mark
The diameter of the base of a cylinder is $4\ cm$ and its height is $14\ cm$. The volume of the cylinder is:
- ✓
$176\ cm^3$
- B
$196\ cm^3$
- C
$276\ cm^3$
- D
$352\ cm^3$
AnswerCorrect option: A. $176\ cm^3$
$176\ cm^3$
View full question & answer→MCQ 181 Mark
The number of solid spheres, each of diameter $6\ cm,$ that can mabe by melting a solid metal cylinder of height $45\ cm$ and diameter $4 \ cm,$ is:
View full question & answer→MCQ 191 Mark
The heights of two circular cylinders of equal volume are in the ratio $1 : 2.$ The ratio of their radii is:
- A
$1:\sqrt{2}$
- ✓
$\sqrt{2}:1$
- C
$1:2$
- D
$1:4$
AnswerCorrect option: B. $\sqrt{2}:1$
$\sqrt{2}:1$
View full question & answer→MCQ 201 Mark
A hollow cube of internal edge $22\ cm$ is filled with spherical marbles of diameter $0.5\ cm$ and $\frac{1}{8}$ space of the cube remains unfilled. Number of marbles required is
- ✓
$142296$
- B
$142396$
- C
$142496$
- D
$142596$
AnswerCorrect option: A. $142296$
$142296$
View full question & answer→MCQ 211 Mark
The height of a cylinder is $14\ cm$ and its curved surface area is $264\ cm^2$. The volume of the cylinder is:
- A
$308\ cm^3$
- ✓
$396\ cm^3$
- C
$1232\ cm^3$
- D
$1848\ cm^3$
AnswerCorrect option: B. $396\ cm^3$
$396\ cm^3$
View full question & answer→MCQ 221 Mark
The volume of a cube is $2744\ cm^2$. Its surface area is:
- A
$196\ cm^2$
- ✓
$1176\ cm^2$
- C
$784\ cm^2$
- D
$588\ cm^2$
AnswerCorrect option: B. $1176\ cm^2$
$1176\ cm^2$
View full question & answer→MCQ 231 Mark
A metallic cone of base radius $2.1\ cm$ and height $8.4\ cm$ is melted and moulded into a sphere. The radius of the sphere is:
- ✓
$2.1\ cm$
- B
$1.05\ cm$
- C
$1.5\ cm$
- D
$2\ cm$
AnswerCorrect option: A. $2.1\ cm$
$2.1\ cm$
View full question & answer→MCQ 241 Mark
The circular ends of a bucket are of radii $35\ cm$ and $14\ cm$ and the height of the bucket is $40\ cm$. Its volume is:
- A
$60060\ cm^3$
- ✓
$80080\ cm^3$
- C
$70040\ cm^3$
- D
$80160\ cm^3$
AnswerCorrect option: B. $80080\ cm^3$
Volume of the buclet $=$ Volume of the frustum of the cone
$=\frac{1}{3}\pi\text{h}[\text{R}^2+\text{r}^2+\text{rr}]$
$=\frac{1}{3}\times\frac{22}{7}\times40[35^2+14^2+(35\times14)]$
$=\frac{880}{21}\times1911$
$=80080\text{ cm}^3$
Hence, the volume of the bucket is $80080\ cm^3.$
View full question & answer→MCQ 251 Mark
The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2cm is:
AnswerThe diameter of such a cone is equal to the edge of the cube.
So, the diameter = 4.2cm.
Hence, the radius = 2.1cm.
View full question & answer→MCQ 261 Mark
The diameter of a sphere is $14\ cm.$ Its volume is:
AnswerCorrect option: C. $1437\frac{1}{3}\text{cm}^3$
Diameter $= 14\ cm$
So, the radius $= 7\ cm$
Volume of the sphere $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times(7)^3$
$=1437\frac{1}{3}\text{cm}^3$
View full question & answer→MCQ 271 Mark
If the radii of the ends of a bucket are $5\ cm$ and $15\ cm$ and it is $24\ cm$ high, then its surface area is:
- A
$1815.3\ cm^2$
- ✓
$1711.3\ cm^2$
- C
$2025.3\ cm^2$
- D
$2360\ cm^2$
AnswerCorrect option: B. $1711.3\ cm^2$
$\text{l}=\sqrt{\text{h}^2+(\text{R}-\text{r})^2}$
$\Rightarrow\text{l}=\sqrt{24^2+(15-5)}$
$\Rightarrow\text{l}=\sqrt{576+100}$
$\Rightarrow\text{l}=\sqrt{676}$
$\Rightarrow\text{l}=26\text{cm}$
Surface area of the bucket
$=\pi\big[\text{r}^2+\text{l}(\text{R}+\text{r})\big]$
$=3.14\times\big[5^2+26(15+5)\big]$
$=3.14\times[545]$
$=1711.3\text{cm}^2$
View full question & answer→Question 281 Mark
Match the following columns:
| |
Column $I$ |
|
Column $II$ |
| $a.$ |
The radii of the circular ends of a bucket, in the form of the frustum of a cone of height $30\ cm,$ are $20\ cm$ and $10\ cm$ respectively. The capacity of the bucket is $ ......cm^3$. |
$p.
$ |
$2418\pi$ |
| $b.$ |
The radii of the circular ends of a conical bucket of height $15\ cm$ are $20$ and $12\ cm$ respectively. The slant height of the bucket is $ ...... \ cm.$ |
$q.$ |
$22000$ |
| $c.$ |
The radii of the circular ends of a solid frustum of a cone are $33\ cm$ and $27\ cm$ and its slant height is $10\ cm$. The total surface area of the bucket is $....cm^2$. |
$r.$ |
$12$ |
| $d.$ |
Three solid metallic spheres of radii $3\ cm, 4\ cm$ and $5\ cm$ are melted to form a single solid sphere. The diameter of the resulting sphere is $...... \ cm.$ |
$s.$ |
$17$ |
Answer
| |
Column $I$ |
|
Column $II$ |
| $a.$ |
The radii of the circular ends of a bucket, in the form of the frustum of a cone of height $30\ cm,$ are $20\ cm$ and $10\ cm$ respectively. The capacity of the bucket is $ ......cm^3$. |
$p.
$ |
$2418\pi$ |
| $b.$ |
The radii of the circular ends of a conical bucket of height $15\ cm$ are $20$ and $12\ cm$ respectively. The slant height of the bucket is $ ...... \ cm.$ |
$q.$ |
$22000$ |
| $c.$ |
The radii of the circular ends of a solid frustum of a cone are $33\ cm$ and $27\ cm$ and its slant height is $10\ cm$. The total surface area of the bucket is $....cm^2$. |
$r.$ |
$12$ |
| $d.$ |
Three solid metallic spheres of radii $3\ cm, 4\ cm$ and $5\ cm$ are melted to form a single solid sphere. The diameter of the resulting sphere is $...... \ cm.$ |
$s.$ |
$17$ |
- Let $R$ and $ r$ be the top and base of the bucket and $h$ be the height.
Capacity of the bucket $=$ Volume of the frustum of the cone
$=\frac{\pi\text{h}}{3}(\text{R}^2+\text{r}^2+\text{Rr})$
$=\frac{22}{7}\times\frac{1}{3}\times30\times(20^2+20^2+20+10)$
$=\frac{220}{7}\times700$
$=22000\text{ cm}^3$
- Slant height, $\text{l}=\sqrt{\text{h}^2+(\text{R}-\text{r})^2}$
$=\sqrt{15^2+(20-12)^2}$
$=\sqrt{225+64}$
$=\sqrt{289}$
$=17\text{ cm}$
- Total surface area of the bucket $=\pi\big[\text{R}^2+\text{r}^2+\text{l}(\text{R}+\text{r})\big]$
$=\pi\big[33^2+27^2+10(33+27)\big]$
$=\pi\big[1089=729+600\big]$
$2418\pi\text{cm}^2$
- Let the diameter be $d.$
So, the radius $=\frac{\text{d}}{2}$
Volume of the sphere $=\frac{4}{3}\pi\text{r}^3=\frac{4}{3}\pi\Big(\frac{\text{d}}{2}\Big)^3$
$\Rightarrow\frac{4}{3}\pi\Big(\frac{\text{d}}{2}\Big)^3=\frac{4}{3}\pi(3)^3+\frac{4}{3}\pi(4)^3+\frac{4}{3}\pi(5)^3$
$\Rightarrow\Big(\frac{\text{d}}{2}\Big)^3=(3)^3+(4)^3+(5)^3$
$\Rightarrow\frac{\text{d}^3}{8}=27+64+125$
$\Rightarrow\frac{\text{d}^3}{8}=216$
$\Rightarrow\text{d}^3=1728$
$\Rightarrow\text{d}=12\text{ cm}$ View full question & answer→MCQ 291 Mark
The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80cm and height 20cm is:
AnswerThe ratio of the total surface area to the lateral surface area
$=\frac{\text{Total surface area}}{\text{Lateral surface area}}$
$=\frac{2\pi\text{r}(\text{h}+\text{r})}{2\pi\text{rh}}$
$=\frac{\text{h+r}}{\text{h}}$
$=\frac{20+80}{20}$
$=\frac{5}{1}$
So, the required ratio is 5 : 1
View full question & answer→MCQ 301 Mark
Assertion and Reason Type
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
|
Assertion (A)
|
Reason (R)
|
|
If the volumes of two spheres are in the ratio 27 : 8 then their surface areas are in the ratio 3: 2.
|
Volume of a sphere $=\frac{4}{3}\pi\text{R}^3.$
Surface area of a sphere $=4\pi\text{R}^2.$
|
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- C
Assertion (A) is true and Reason (R) is false.
- ✓
Assertion (A) is false and Reason (R) is true.
AnswerCorrect option: D. Assertion (A) is false and Reason (R) is true.
Let r and R be the radii of the two sheres.
Ratio of their volumes $=\frac{27}{8}$
$\Rightarrow\frac{\frac{4}{3}\pi\text{r}^3}{\frac{4}{3}\pi\text{R}^3}=\frac{27}{8}$
$\Rightarrow\frac{\text{r}^3}{\text{R}^3}=\frac{27}{8}$
$\Rightarrow\frac{\text{r}}{\text{R}}=\frac{3}{2}$
Ratio of their surface areas $=\frac{4\pi\text{r}^2}{4\pi\text{R}^2}$
$=\Big(\frac{\text{r}}{\text{R}}\Big)^2$
$=\Big(\frac{3}{2}\Big)^2$
$=\frac{9}{4}$
So, the Assertion (A) is false.
The reason (R)s true.
View full question & answer→MCQ 311 Mark
The radius of the base of a cone is 5cm and its height is 12cm. Its curved surface area is:
- A
$60\pi\text{cm}^2$
- ✓
$65\pi\text{cm}^2$
- C
$30\pi\text{cm}^2$
- D
$\text{None of these}$
AnswerCorrect option: B. $65\pi\text{cm}^2$
Slant height, $\text{l}=\sqrt{\text{r}^2+\text{h}^2}$
$\Rightarrow\text{l}=\sqrt{5^2+12^2}$
$\Rightarrow\text{l}=\sqrt{25+144}$
$\Rightarrow\text{l}=\sqrt{169}$
$\Rightarrow\text{l}=13\text{cm}$
Curved surface area of the cone $=\pi\text{rl}$
$=\pi\times5\times13$
$=65\pi\text{cm}^2$
View full question & answer→MCQ 321 Mark
The surface areas of two spheres are in $e$ ratio $16: 9$. The ratio o their volumes is:
- ✓
$64 : 27$
- B
$16 : 9$
- C
$4 : 3$
- D
$16^3 : 9^3$
AnswerCorrect option: A. $64 : 27$
Given that the surface areas of the two spheres are in the ratio $16 : 9.$
So, $\frac{4\pi\text{r}^2}{4\pi\text{R}^2}=\frac{16}{9}$
$\Rightarrow\frac{\text{r}^2}{\text{R}^2}=\frac{16}{9}$
$\Rightarrow\frac{\text{r}}{\text{R}}=\frac{4}{3}$
Let the volume of the sphere with radius $r$ and $R$ be $V _1$ and $V _2$ respectively.
$\frac{\text{V}_1}{\text{V}_2}=\frac{\frac{4}{3}\pi\text{r}^3}{\frac{4}{3}\pi\text{R}^3}$
$\Rightarrow\frac{\text{V}_1}{\text{V}_2}=\Big(\frac{\text{r}}{\text{R}}\Big)^3$
$\Rightarrow\frac{\text{V}_1}{\text{V}_2}=\Big(\frac{4}{3}\Big)^3=\frac{64}{27}$
Hence, the ratio of their volumes is $64.27$.
View full question & answer→MCQ 331 Mark
The diameters of two circular ends of a bucket are 44cm and 24cm, and the height of the bucket is 35cm. The capacity of the bucket is:
AnswerSince the diameter of the circular ends of the bucket are 44cm and 24cm, the radii of thr circular end are 22cm and 12cm.
Capacity of the bucket = volume of the bucket
$=\frac{1}{3}\pi\text{h}\big[\text{R}^2+\text{r}^2+\text{Rr}\big]$
$=\frac{1}{3}\times\frac{22}{7}\times35\times\big[22^2+12^2+(22\times12)\big]$
$=32.7\text{ litres}$
Hence, the capacity of the bucket is 32.7 litres.
View full question & answer→MCQ 341 Mark
A metallic spherical shell of internal and external diameters 4cm and 8cm, respectively, is melted and recast in the form of a cone of base diameter 8cm. The height of the cone is:
AnswerThe radii od the spherical shell is 2cm and 2cm.
Volume of the spherical shell $=\frac{4}{3}\pi\big(\text{R}^3-\text{r}^3\big)$
$=\frac{4}{3}\pi\big(\text{R}^3-\text{2}^3\big)$
$=\frac{4}{3}\pi(56)$
Radius of the cone = 4cm
Volume of the cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi(4)^2\text{h}$
$\Rightarrow16\text{h}=4(56)$
$\Rightarrow\text{h}=14\text{cm}$
View full question & answer→MCQ 351 Mark
A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left over is called:
AnswerA cone is cut by a plane parallel to its base the upper part is remove. part that is left over is called the frutum of a cone.
View full question & answer→MCQ 361 Mark
The height of a conical tent is $14m$ and its floor area is $346.5m^2$. How much canvas, $1.1$ wide, will be required for it?
- A
$490m$
- ✓
$525m$
- C
$665m$
- D
$860m$
AnswerCorrect option: B. $525m$
Area of the floor of a conical tent $=\pi(\text{r})^2$
$\Rightarrow\pi\text{r}^2=346.5$
$\Rightarrow\text{r}^2=\Big(\frac{3465}{10}\times\frac{7}{22}\Big)$
$\Rightarrow\text{r}^2=\frac{441}{4}$
$\Rightarrow\frac{21}{2}\text{cm}$
Slant height of the cone, $\text{l}=\sqrt{\text{r}^2+\text{h}^2}$
$\Rightarrow\text{l}=\sqrt{\Big(\frac{21}{2}\Big)^2+14^2}$
$\Rightarrow\text{l}=\sqrt{\frac{1225}{4}}$
$\Rightarrow\text{l}=\frac{32}{2}\text{m}$
Area of the canvas = curved surface area of the conical tent
$\Rightarrow$ Area of the canvas $=\pi\text{r}\text{l}$
$\Rightarrow$ Area of the canvas $=\frac{22}{7}\times\frac{21}{2}\times\frac{35}{2}=577.5\text{m}^2$
Lenght of the canvas $=\frac{\text{Area of the canvas}}{\text{Width of the canvas}}$
$=\frac{577.5}{1.1}$
$=525\text{m}$
View full question & answer→MCQ 371 Mark
A rectangular sheet of paper 40cm × 22cm, is rolled to form a allow cylinder of height 40cm. The radius of e cylinder {in cth) is:
AnswerSince the height of the cylinder is given to be 40cm, the sheet to paper when converted to a cylinder,
Has its circum ference to be 22cm.
So, circum ference = 22cm
$\Rightarrow2\pi\text{r}=22$
$\Rightarrow2\times\frac{22}{7}\times\text{r}=22$
$\Rightarrow\text{r}=3.5\text{cm}$
Hence, the radius of the cylinder is 3.5cm.
View full question & answer→MCQ 381 Mark
Assertion and Reason Type
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
|
Assertion (A)
|
Reason (R)
|
|
If the radii of the circular ends of a bucket 24cm high are 15cm and 5cm respectively, then the surface area of the bucket is $545\pi\text{cm}^2.$
|
if the radii of the circular ends of the frustum of a cone are R and r respectively and its height is h, surface area is:
$\pi\big\{\text{R}^2+\text{r}^2+\text{l}(\text{R}-\text{r})\big\}$
where $\text{l}^2=\text{h}^2+(\text{R}+\text{r})^2.$
|
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- C
Assertion (A) is true and Reason (R) is false.
- ✓
Assertion (A) is false and Reason (R) is true.
AnswerCorrect option: D. Assertion (A) is false and Reason (R) is true.
Slant height $=\sqrt{\text{h}^2+(\text{R}-\text{r})^2}$
$=\sqrt{24^2+(15-5)^2}$
$=\sqrt{576+100}$
$=\sqrt{676}$
$=26\text{cm}$
Surface area of the bucket $=\big[\text{R}^2+\text{r}^2+\text{l}(\text{R}+\text{r})\big]$
$=\pi\big[15^2+5^2+26(15+5)\big]$
$=\pi\big[225+25+520\big]$
$=770\pi\text{cm}^2$
The Assertion (A) and the Reason (R) are incorrect.
Note: The answer given in the text is incorrect.
View full question & answer→MCQ 391 Mark
The area of the base of a right circular cone is $154\ cm^2$ and its height is $14\ cm.$ Its curved surface area is:
- ✓
$154\sqrt{5}\text{cm}^2$
- B
$154\sqrt{7}\text{cm}^2$
- C
$77\sqrt{7}\text{cm}^2$
- D
$77\sqrt{5}\text{cm}^2$
AnswerCorrect option: A. $154\sqrt{5}\text{cm}^2$
Area of the base of the cone $= 154$
$\Rightarrow\pi\text{r}^2=154$
$\Rightarrow\frac{22}{7}\times\text{r}^2=154$
$\Rightarrow\text{r}^2=49$
$\Rightarrow\text{r}=7\text{cm}$
$\text{l}=\sqrt{\text{r}^2+\text{h}^2}$
$\Rightarrow\text{l}=\sqrt{7^2+14^2}$
$\Rightarrow\text{l}=\sqrt{49+196}$
$\Rightarrow\text{l}=\sqrt{245}$
$\Rightarrow\text{l}=7\sqrt{5}\text{cm}$
Curve surface area of the cone $=\pi\text{rl}$
$=\frac{22}{7}\times7\times7\sqrt{5}$
$=154\sqrt{5}\text{cm}^2$
View full question & answer→MCQ 401 Mark
The ratio between the volume of two spheres is 8 : 27. What is the ratio between their surface areas?
AnswerLet the radii of the spheres be R and r.
Ratio of volumes $=\frac{\frac{4}{3}\pi\text{R}^3}{\frac{4}{3}\pi\text{r}^3}$
$\Rightarrow\frac{\frac{4}{3}\pi\text{R}^3}{\frac{4}{3}\pi\text{r}^3}=\frac{8}{27}$
$\Rightarrow\Big(\frac{\text{R}}{\text{r}}\Big)^3=\Big(\frac{2}{3}\Big)^3$
$\Rightarrow\frac{\text{R}}{\text{r}}=\frac{2}{3}$
Ratio between their surface areas
$=\frac{4\pi\text{R}^2}{4\pi\text{r}^2}$
$\Rightarrow\Big(\frac{\text{R}}{\text{r}}\Big)^2$
$=\Big(\frac{2}{3}\Big)^2$
$=\frac{4}{9}$
View full question & answer→MCQ 411 Mark
The total surface area of a cube is $864\ cm^2$. Its volume is:
- A
$3456\ cm^3$
- B
$432\ cm^3$
- ✓
$1728\ cm^3$
- D
$3456\ cm^3$
AnswerCorrect option: C. $1728\ cm^3$
Let the edge iof the cube be $x \ cm$.
Total surface area of a cube $=6 x^2$
$\Rightarrow 6 x^2=864$
$\Rightarrow x^2=144$
$\Rightarrow x=12 \ cm$
So, the volume of the cube $=x^3$
$=(12)^3$
$=1728 \ cm^3$
View full question & answer→MCQ 421 Mark
A medicine capsule is in the shape of a cylinder of diameter $0.5\ cm$ with a hemisphere tucked at each end. The length of the entire capsule is $2\ cm.$ The capacity of the capsule is:
- A
$0.33 \ cm^2$
- B
$0.34 \ cm^2$
- C
$0.35 \ cm^2$
- ✓
$0.36 \ cm^2$
AnswerCorrect option: D. $0.36 \ cm^2$
Radiud of the capsule $= 0.25\ cm$
Let the length of the cylindrical part of the capsule be $x \ cm.$
So, $0.25 + x + 0.25 = 2$
$\Rightarrow 0.5 + x = 2$
$\Rightarrow x = 1.5$
Capacity of the capsule
$= 2 \times ($ Volume of the hemisphere$) + ($ Volume of the cylinder$)$
$=2\times\Big(\frac{2}{3}\pi\text{r}^3\Big)+(\pi\text{r}^2\text{h})$
$=2\times\Big(\frac{2}{3}\times\frac{22}{7}\times0.25^3\Big)+\Big(\frac{22}{7}\times0.25^2\times1.5\Big)$
$=0.36\text{cm}^2$
View full question & answer→MCQ 431 Mark
The slant height of a bucket is $45\ cm$ and the radii of its top and bottom are $28\ cm$ and $7\ cm,$ respectively. The curved surface area of the bucket is:
- A
$4953 \ cm^2$
- B
$4952 \ cm^2$
- C
$4951 \ cm^2$
- ✓
$4950 \ cm^2$
AnswerCorrect option: D. $4950 \ cm^2$
The curved surface area of the bucket.
$=\pi\text{l}(\text{R}+\text{r})$
$=\frac{22}{7}\times45\times(28+7)$
$=4950\text{cm}^2$
Hence, the curved surface area of the bucket is $4950\ cm^2.$
View full question & answer→MCQ 441 Mark
The sum of length, breadth and height of a cuboid is 19cm and its diagonal is $\sqrt[5]{5}\text{cm}.$ Its surface area is
- A
$361cm^2$
- B
$125cm^2$
- ✓
$236cm^2$
- D
$486cm^2$
AnswerCorrect option: C. $236cm^2$
$\text { Given that } I+b+h=19$$\Rightarrow(I+b+h)^2=19^2$
$\Rightarrow I^2+b^2+h^2+2 l b+2 bh+2 l=361$
$\Rightarrow I^2+b^2+h^2+2(lb+bh+l h)=361$
Wen know that, the diagonal of a cuboid $=L^2+b^2+h^2$
That is, $(5 \sqrt{5})^2= l ^2+ b ^2+ h ^2$
So, from (i), we get
$(5 \sqrt{5})^2+2(lb+bh+lh)=361$
$\Rightarrow 125+2(lb+bh+lh)=361$
$\Rightarrow 2(lb+bh+lh)=236$
$\Rightarrow \text { Sirface area }=236 cm^2$
Hence, the surface area of the cuboid is $236 cm^2$
View full question & answer→MCQ 451 Mark
The volume of a hemisphere is $19404\ cm^3$. The total surface area of the hemisphere is:
- ✓
$4158\ cm^2$
- B
$16632\ cm^2$
- C
$8316\ cm^2$
- D
$3696\ cm^2$
AnswerCorrect option: A. $4158\ cm^2$
Volume of hemisphere $=\frac{2}{3}\pi\text{r}^3$
$\frac{2}{3}\pi\text{r}^3=19404$
$\frac{2}{3}\times\frac{22}{7}\text{r}^3=19404$
$\text{r}^3=19404\times\frac{3\times7}{2\times22}$
$\text{r}^3=9261$
$\text{r}^3=21^3$
$\text{r}=21\text{cm}$
Surface area of hemisphere $=3\pi\text{r}^2$
$=3\times\frac{22}{7}\times21^2$
$=4158\text{cm}^2$
View full question & answer→MCQ 461 Mark
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is:
AnswerLet the radii of the two cylinders be 2x and 3x,
and the heights of the two cylinders be 5y and 3y respectively
Ratio of the volume of the cylinders $=\frac{\pi(2\text{x})^2(5\text{y})}{\pi(3\text{x})^2(3\text{y})}$
$=\frac{20}{27}$
That is, the ratio of their volume is 20 : 27.
View full question & answer→MCQ 471 Mark
During conversion of a solid from one shape to another, the volume of the new shape will:
AnswerDuring conversion of a solid from one shape to another, the volume of the new shape will remain altered.
View full question & answer→MCQ 481 Mark
A surahi is a combination of:
- ✓
- B
A hemisphere and a cylinder.
- C
- D
AnswerA surahi is a combination of a sphere and a cylinder, the lower portion is the sphere and the upper portion is the cylinder.
View full question & answer→MCQ 491 Mark
Assertion and Reason Type
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
|
Assertion (A)
|
Reason (R)
|
|
A hemisphere of radius 7cm is to be painted outside on the surface. The total cost of painting at ₹ 5 per $cm^2$ is ₹ 2300.
|
The total surface volume of a hemisphere is $3\pi\text{r}^2.$
|
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- C
Assertion (A) is true and Reason (R) is false.
- ✓
Assertion (A) is false and Reason (R) is true.
AnswerCorrect option: D. Assertion (A) is false and Reason (R) is true.
The total surface area of the hemisphere
$=\pi\text{r}^2+2\pi\text{r}^2$
$=2\pi\text{r}^2$
$=3\times\frac{22}{7}\times7\times7$
$=462\text{cm}^2$
Cost of painting at Rs. 5 per $cm^2$ = Rs. (462 × 5) = Rs. 2310
So, the Assertion (A) is false.
The Reason (R) is true.
View full question & answer→MCQ 501 Mark
Assertion and Reason Type
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
|
Assertion (A)
|
Reason (R)
|
|
The number of coins of 1.75cm in diameter and 2 mm thick from a melted cuboid (10cm × 5.5cm × 3.5cm) is 400.
|
Volume of a cylinder of base radius r and height h is given by $\text{V}=(\pi\text{r}^2\text{h})$ cubic units. And volume of a cuboid = (l × b × h) cubic units.
|
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- C
Assertion (A) is true and Reason (R) is false.
- D
Assertion (A) is false and Reason (R) is true.
AnswerCorrect option: A. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
Volume of the cuboid $=(10\times5.5\times3.5)\text{cm}^3$
Volume of each cone $=\pi\text{r}^2\text{h}$
$=\frac{22}{7}\times\frac{1.75}{2}\times\frac{1.75}{2}\times\frac{1}{5}$
Number of cone $=\frac{\text{volume of the cuboid}}{\text{Volume of each coin}}$
$=\frac{10\times5.5\times3.5}{\frac{22}{7}\times\frac{1.75}{2}\times\frac{1.75}{2}\times\frac{1}{5}}$
$=400$
So, the Assertion (A) is true.
The Reason (R) is also true and is the correct explanation for the Assertion (A).
View full question & answer→