MCQ 11 Mark
The diagonal of a cube measures $4\sqrt{3}\text{cm}.$ Its volume is:
- A
$8 \mathrm{~cm}^3$
- B
$16 \mathrm{~cm}^3$
- C
$27 \mathrm{~cm}^3$
- ✓
$64 \mathrm{~cm}^3$
AnswerCorrect option: D. $64 \mathrm{~cm}^3$
Diagonal of cube $4\sqrt{3}$
Side $=\frac{4\sqrt{3}}{3}$
$= 4\ cm$
Volume $= a^3= (4)^3$
$= 64\ cm^3$
View full question & answer→MCQ 21 Mark
Five equal cubes, each of edge $5\ cm,$ are placed adjacent to each other. The volume of the cuboid so formed, is:
- A
$ 125 \mathrm{~cm}^3 $
- B
$ 375 \mathrm{~cm}^3 $
- C
$ 525 \mathrm{~cm}^3 $
- ✓
$ 625 \mathrm{~cm}^3 $
AnswerCorrect option: D. $ 625 \mathrm{~cm}^3 $
Each edge of $5$ cubes $= 5\ cm$
Placing than adjecent to each other,
Length of new cuboid$ (l)$
$= 5 \times 5 = 25\ cm$
Breadth $(b) = 5\ cm$
And height $(h) = 5\ cm$
Volume of new cuboid $= lbh$
$= 25 \times 5 \times 5\ cm^3$
$= 625 \mathrm{~cm}^3 $
View full question & answer→MCQ 31 Mark
The ratio of the radii of two cylinders is $2 : 3$ and the ratio of their heights is $5 : 3.$ The ratio of their volumes will be:
- A
$4 : 9$
- B
$9 : 4$
- ✓
$20 : 27$
- D
$27 : 20$
AnswerCorrect option: C. $20 : 27$
Ratio in radii of two cylinder $= 2 : 3$
And ratio in their height $= 5 : 3$
Let radii of two cylinder $= 2x$ and $3x,$
And corresponding height $= 5y, 3y$
$\therefore\frac{\text{Volume of frist cylinder}}{\text{Volume of second cylinder}}$
$=\frac{\pi\text{r}^2_1\text{h}_1}{\pi\text{r}^2_2\text{h}_1}=\frac{(2\text{x})^2\times5\text{y}}{(3\text{x})^2\times3\text{y}}$
$=\frac{4\text{x}^2\times5\text{y}}{9\text{x}^2\times3\text{y}}=\frac{20\text{x}^2.\text{y}}{27\text{x}^2\text{y}}=\frac{20}{27}$
$\therefore\text{Ratio}=20:27$
View full question & answer→MCQ 41 Mark
The diameter of a cylinder is $14\ cm$ and its curved surface area is $220\ cm^2$. The volume of the cylinder is:
- ✓
$770 \mathrm{~cm}^3$
- B
$1000 \mathrm{~cm}^3$
- C
$1540 \mathrm{~cm}^3$
- D
$6622 \mathrm{~cm}^3$
AnswerCorrect option: A. $770 \mathrm{~cm}^3$
Dieameter of cylinder $= 14\ cm$
Radius $(r) = 7 \ cm$
Curved surface area $ = 220\ cm^2$
$\therefore$ Height $(h) =\frac{\text{Surface area}}{2\pi\text{h}}$
$=\frac{220\times7}{2\times22\times7}=5\text{cm}$
$\therefore\text{Volume}=\pi\text{r}^2\text{h}=\frac{22}{7}\times7\times7\times5\text{cm}^3$
$=770\text{cm}^3$
View full question & answer→MCQ 51 Mark
The surface area of a $(10\ cm \times 4\ cm \times 3\ cm)$ brick is:
- A
$ 84 \mathrm{~cm}^2 $
- B
$ 124 \mathrm{~cm}^2$
- ✓
$164 \mathrm{~cm}^2 $
- D
$ 180 \mathrm{~cm}^2 $
AnswerCorrect option: C. $164 \mathrm{~cm}^2 $
Surface area of a brick of measure $10\ cm \times 4\ cm \times 3\ cm,$
$= 2(l \times b + b \times h + h \times l)$
$= 2[10 \times 4 + 4 \times 3 + 3 \times 10]cm^2$
$= 2[40 + 12 + 30]$
$= 82 \times 2$
$= 164 \mathrm{~cm}^2 $
View full question & answer→MCQ 61 Mark
A rectangular water reservoir contains $42000$ litres of water. If the length of reservoir is $6m$ and its breadth is $3.5m,$ the depth of the reservoir is:
AnswerWater in rectangular reservoir $= 42000$
Volume $=\frac{42000}{1000}=42\text{m}^3$
Length $(l) = 6m,$
Breadth $(b) = 3.5m$
Depth $=\frac{\text{Volume}}{\text{l}\times\text{b}}$
$=\frac{42}{6\times3.5}$
$=2\text{m}$
View full question & answer→MCQ 71 Mark
An iron beam is $9m$ long, $40\ cm$ wide and $20\ cm$ high. If $1$ cubic metre of iron weighs $50\ kg,$ what is the weight of the beam?
- A
$56\ kg$
- B
$48\ kg$
- ✓
$36\ kg$
- D
$27\ kg$
AnswerCorrect option: C. $36\ kg$
Length $(b) = 40\ cm$ $=\frac{40}{100}\text{m}=\frac{2}{5}\text{m}$
And height $(h) = 20\ cm$ $=\frac{20}{100}=\frac{1}{5}\text{m}$
$\therefore$ Volume $= lbh=9\times\frac{2}{5}\times\frac{1}{5}=\frac{18}{25}\text{m}^3$
Weight of $1$ cubic $m = 50\ kg.$
Total weight of beam $=\frac{18}{25}\times25$
$= 36\ kg$
View full question & answer→MCQ 81 Mark
Two cubes have their volumes in the ratio $1 : 27.$ The ratio of their surface areas is:
- A
$1 : 3$
- ✓
$1 : 9$
- C
$1 : 27$
- D
AnswerCorrect option: B. $1 : 9$
Ratio in the two volume $= 1 : 27$
Let volume of frist volume $= x^3$
And volume of second volume $= 27x^3$
Side of frist cube $= x$
And side of second cube $\sqrt[3]{27\text{x}^3}=3\text{x}$
$\text{Now}\frac{\text{Surface area of frist cube}}{\text{Surface area of second cube}}$
$=\frac{6\text{x}^2}{6(3\text{x})^2}$
$=\frac{6\text{x}^2}{6\times9\text{x}^2}=\frac{1}{9}$
$\therefore\text{Ratio}=1:9$
View full question & answer→MCQ 91 Mark
The cost of painting the whole surface area of a cube at the rate of $10$ paise per $cm^2$ is $Rs. 264.60.$ Then, the volume of the cube is:
- A
$6859 \mathrm{~cm}^3 $
- ✓
$9261 \mathrm{~cm}^3 $
- C
$8000 \mathrm{~cm}^3 $
- D
$10648 \mathrm{~cm}^3 $
AnswerCorrect option: B. $9261 \mathrm{~cm}^3 $
Rate of painting $= 10$ paise per $cm^2$
Total cost $= Rs. 264.60$
$\therefore$ Total surface area $=\frac{264.60}{10}\text{cm}^3$
$=\frac{26460}{10}=2646\text{cm}^2$
$\therefore\text{Side}=\sqrt{\frac{2646}{6}}=\sqrt{441}=21\text{cm}$
Volume $= a^3= (21)^3= 9261\ cm^3$
View full question & answer→MCQ 101 Mark
Three cubes of iron whose edges are $6\ cm, 8\ cm$ and $10\ cm$ respectively are melted and formed into a single cube. The edge of the new cube formed is:
- ✓
$12\ cm$
- B
$14\ cm$
- C
$16\ cm$
- D
$18\ cm$
AnswerCorrect option: A. $12\ cm$
Sides $($edges$)$ of $3$ cubes are $6\ cm, 8\ cm,$ and $10\ cm$ respectively.
Volume of frist cube $= (6)^3 = 216\ cm^3$
Volume of second cube $= (8)^3= 512\ cm^3$
And volume of third cube,
$= (10)^3= 1000\ cm^3$
Sum of volumes of $3$ cubes $= 216 + 512 + 1000$
$= 1728\ cm^3$
Volume of new single cube $= 1728\ cm^3$
Edge $=\sqrt[3]{1728}$
$=\sqrt[3]{(12)^3}$
$=12\text{cm}$
View full question & answer→MCQ 111 Mark
Mark against the correct answer in the following: the area of the base of a circular cylinder is $35\ cm^2$ and its height is $8\ cm.$ The volume of the cylinder is:
- A
$140 \mathrm{~cm}^3 $
- ✓
$280 \mathrm{~cm}^3 $
- C
$420 \mathrm{~cm}^3 $
- D
$210 \mathrm{~cm}^3 $
AnswerCorrect option: B. $280 \mathrm{~cm}^3 $
Area $= 35\ cm^2$
Height $= 8\ cm$
$\therefore$ Volume $=$ base area $\times $ height $= 35 \times 8 = 280\ cm^3$.
View full question & answer→MCQ 121 Mark
The maximum length of a pencil that can be kept in a rectangular box of dimensions $12cm × 9cm × 8cm,$ is:
- A
$13cm$
- ✓
$17cm$
- C
$18cm$
- D
$19cm$
AnswerCorrect option: B. $17cm$
Length $(l) = 12cm$
Breadth $(b) = 9cm$
Height $(h) = 8cm$
$\therefore$ Miaximum length of diagonal (pencil)
$=\sqrt{\text{l}^2+\text{b}^2+\text{a}^2}$
$=\sqrt{(12)^2+(9)^2+(8)^2}$
$=\sqrt{144+81+64}$
$=\sqrt{289}=17\text{cm}$
View full question & answer→MCQ 131 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 \mathrm{~cm}^3 $
- ✓
$ 396 \mathrm{~cm}^3 $
- C
$ 1232 \mathrm{~cm}^3 $
- D
$ 1848 \mathrm{~cm}^3 $
AnswerCorrect option: B. $ 396 \mathrm{~cm}^3 $
Curved surface area of a cylinder $= 264\ cm^3$
Height $(h) = 14\ cm$
$\therefore$ Radius $(r) =\frac{\text{Surface area}}{2\pi\text{h}}$
$=\frac{264\times7}{2\times22\times14}\text{cm}=3\text{cm}$
Now volume $=\pi\text{r}^2\text{h}=\frac{22}{7}\times3\times3\times14\text{cm}^3=396\text{cm}^3$
View full question & answer→MCQ 141 Mark
Mark against the correct answer in the following: The dimensions of a cuboid are $8m, 6m, 4m.$ Its lateral surface area is:
- A
$ 210 \mathrm{~m}^2 $
- B
$ 105 \mathrm{~m}^2 $
- ✓
$ 112 \mathrm{~m}^2 $
- D
$240 \mathrm{~m}^2 $
AnswerCorrect option: C. $ 112 \mathrm{~m}^2 $
Lateral surface area $= 2((l + b) \times h) = 2((8 + 6) \times 4) =2(56) = 112 \mathrm{~m}^2 $
View full question & answer→MCQ 151 Mark
The edges of a cuboid are in the ratio $1 : 2 : 3$ and its surface area is $88\ cm^2$. The volume of the cuboid is:
- ✓
$ 48 \mathrm{~cm}^3 $
- B
$ 64 \mathrm{~cm}^3 $
- C
$ 96 \mathrm{~cm}^3 $
- D
$ 120 \mathrm{~cm}^3 $
AnswerCorrect option: A. $ 48 \mathrm{~cm}^3 $
Ratio in sides of a cuboid $= 1 : 2 : 3$
Surface area $= 88\ cm^2$
Let $l = x,$
$ b = 2x$ and $h = 3x$
Then $ 2(lb + hl) = 88$
$\Rightarrow 2(2x^2+ 6x^2+ 3x^2) = 88$
$\Rightarrow 2 \times 11x^2= 88$
$\Rightarrow\text{x}^2=\frac{88}{22}=4=(2)^2$
$\Rightarrow x = 2$
$\Rightarrow l = 2\ cm, b = 2x = 2 \times 2 = 4\ cm$
And $h = 3x = 3 \times 2 = 6\ cm$
Now volume $= l.b.h = 2 \times 4 \times 6\ cm^3$
$= 48\ cm^3$
View full question & answer→MCQ 161 Mark
The diagonal of a cube is $9\sqrt{3}$ long. Its total surface area is:
- A
$243 \mathrm{~cm}^2$
- ✓
$486 \mathrm{~cm}^2$
- C
$324 \mathrm{~cm}^2$
- D
$648 \mathrm{~cm}^2$
AnswerCorrect option: B. $486 \mathrm{~cm}^2$
Diagonals of cube $9\sqrt{3}\text{cm}$
Side $=\frac{9\sqrt{3}}{\sqrt{3}}$
$= 9\ cm$
Surface area $= 6a^2$
$= 6(9)^2= 6 \times 81\ cm^2$
$= 486\ cm^2$
View full question & answer→MCQ 171 Mark
The number of coins, each of radius $0.75\ cm$ and thickness $0.2\ cm,$ to be melted to make a right circular cylinder of height $8\ cm$ and base radius $3 \ cm$ is:
AnswerRadius of each $(r) = 0.75\ cm$
And thickness $(h) = 0.2\ cm$
$\therefore$ Then volume $=\pi\text{r}^2\text{h}=\pi\times\frac{75}{100}\times\frac{75}{100}\times\frac{2}{10}\text{cm}^3$
$=\pi\times\frac{3}{4}\times\frac{3}{4}\times\frac{1}{5}=\frac{9}{80}\pi\text{ cm}^3$
Volume of cylinder whose radius $= 3\ cm$
And height $8\ cm=\pi(3)^3\times8\text{cm}^3$
$=72\pi\text{ cm}^3$
$\therefore$ No. of coin $=\frac{72\pi\times80}{9\pi}=640$
View full question & answer→MCQ 181 Mark
The total surface area of a cube is $150\ cm^2$. Its volume is:
- A
$216 \mathrm{~cm}^3 $
- ✓
$ 125 \mathrm{~cm}^3 $
- C
$ 64 \mathrm{~cm}^3 $
- D
$ 1000 \mathrm{~cm}^3 $
AnswerCorrect option: B. $ 125 \mathrm{~cm}^3 $
Total surface area of cube $= 150\ cm^2$
Side $=\sqrt{\frac{150}{6}}$
$=\sqrt{25}$
$=5\text{cm}$
Volume $= ($side$)^3$
$= (5)^3$
$= 125\ cm^3$
View full question & answer→MCQ 191 Mark
The dimensions of a room are $(10m \times 8m \times 3.3m).$ How many men can be accommodated in this room if each man requires $3m^3$ of space?
AnswerDiamensions of a room are $10m, 8m, 3.3m$
Volume of air in it $= lbh$
$= 10 \times 8 \times 3.3 = 264m^3$
No, of men $=\frac{264}{3}$
$= 88$
View full question & answer→MCQ 201 Mark
The height of a cylinder is $80\ cm$ and the diameter of its base is $7\ cm.$ The whole surface area of the cylinder is:
- ✓
$1837 \mathrm{~cm}^2$
- B
$1760 \mathrm{~cm}^2$
- C
$1942 \mathrm{~cm}^2$
- D
$3080 \mathrm{~cm}^2$
AnswerCorrect option: A. $1837 \mathrm{~cm}^2$
Diameter of cylinder $= 7\ cm$
Radius $(r) =\frac{7}{2}\text{cm}$
Height $(h) = 80\ cm$
$\therefore$ Total surface area $=2\pi\text{r} (\text{h}+\text{r})$
$=2\times\frac{22}{7}\times\frac{7}{2}\Big(80+\frac{7}{2}\Big)\text{cm}^2$
$=22\Big(\frac{167}{2}\Big)$
$=1837\text{cm}^2$
View full question & answer→MCQ 211 Mark
A circular well with a diameter of $2$ metres, is dug to a depth of $14$ metres. What is the volume of the earth dug out$?$
- A
$32 \mathrm {~m}^3$
- B
$36 \mathrm{~m}^3$
- C
$40 \mathrm{~m}^3$
- ✓
$44 \mathrm{~m}^3$
AnswerCorrect option: D. $44 \mathrm{~m}^3$
Diameter of circular well $= 2n$
Radius $=\frac{2}{2}=1\text{m}$
Depth $(h) = 14m$
Volume of earth dug out $=\pi\text{r}^2\text{h}$
$=\frac{22}{7}\times1\times1\times14$
$=44\text{m}^3$
View full question & answer→MCQ 221 Mark
The height of a cylinder is $14\ cm$ and its diameter is $10\ cm.$ The volume of the cylinder is:
- ✓
$ 1100 \mathrm{~cm}^3 $
- B
$ 3300 \mathrm{~cm}^3 $
- C
$ 3500 \mathrm{~cm}^3 $
- D
$ 7700 \mathrm{~cm}^3 $
AnswerCorrect option: A. $ 1100 \mathrm{~cm}^3 $
Diameter of cylinder $= 10\ cm$
Radius $(r) =\frac{10}{2}=5\text{cm}$
Height $(h) = 14\ cm$
$\therefore$ Volume $=\pi\text{r}^2\text{h}$
$=\frac{22}{7}\times5\times5\times14\text{cm}^3$
$=1100\text{cm}^3$
View full question & answer→MCQ 231 Mark
The ratio of the total surface area to the lateral surface area of a cylinder whose radius is $20\ cm$ and height $60\ cm,$ is:
- A
$2 : 1$
- B
$3 : 2$
- ✓
$4 : 3$
- D
$5 : 3$
AnswerCorrect option: C. $4 : 3$
Radius of a cylinder $(r) = 20\ cm$
And height $(h) = 60\ cm$
$\therefore$ Leteral surface area $=2\pi\text{rh}$
$=2\times\pi\times20\times60=24000\pi$
And total surface area $=2\pi\text{rh }+2\pi\text{h} ^2$
$=24000\pi+2\pi\times20\times20$
$=24000\pi+800\pi=3200\pi$
$\therefore$ Ratio $3200\pi:2400\pi$
$\Rightarrow4:3$
View full question & answer→MCQ 241 Mark
How many cubes of $10\ cm$ edge can be put in a cubical box of $1m$ edge$?$
- A
$10$
- B
$100$
- ✓
$1000$
- D
$10000$
AnswerCorrect option: C. $1000$
Edge of cube $= 10\ cm$
Volume $= a^3= (10)^3= 1000\ cm^3$
Edge of box $= 1m = 100\ cm$
$\therefore$ Volume $= (100)^3= 1000000\ cm^3$
No. of cubes $=\frac{1000000}{1000}=1000$
View full question & answer→MCQ 251 Mark
If each side of a cube is doubled then its volume:
- A
- B
Becomes $4$ times.
- C
Becomes $6$ times.
- ✓
Becomes $8$ times.
AnswerCorrect option: D. Becomes $8$ times.
Let side of cube in frist case $= a$
Then volume $= a^3$
If side of cube is doubled, then side $= 2a$
Volume $(2a)^3 = 8a^3$
Becomes $8$ times.
View full question & answer→MCQ 261 Mark
Mark against the correct answer in the following: A cuboid having dimensions $16m × 11m × 8m$ is melted to form a cylinder of radius $4m.$ What is the height of the cylinder$?$
AnswerVolume of the cuboid $= 16 \times 11 \times 8 = 1408m^3$
Volume of the cylinder $=\pi\text{r}^2\text{h}=1408\text{m}^3$
$\therefore\text{h}=\frac{1408\times7}{22\times4\times4}=28\text{m}$
View full question & answer→MCQ 271 Mark
A rectangular water tank is $3m$ long, $2m$ wide and $5m$ high. How many litres of water can it hold ?
- ✓
$30000$
- B
$15000$
- C
$25000$
- D
$35000$
AnswerCorrect option: A. $30000$
Length of water tank $(l) = 3m$
Width $(b) = 2m$
And height $(h) = 5m$
Volume $= lbh = 3 \times 2 \times 5 = 30m^3$
Water in it $= 30 \times 1000$
$= 30000$
View full question & answer→MCQ 281 Mark
Mark against the correct answer in the following : The surface area of a cube is $384\ cm^2$. Its volume is :
- ✓
$512 \mathrm{~cm}^3$
- B
$256 \mathrm{~cm}^3$
- C
$384 \mathrm{~cm}^3$
- D
$320 \mathrm{~cm}^3$
AnswerCorrect option: A. $512 \mathrm{~cm}^3$
Surface area $= 6a^2$
$\Rightarrow6\text{a}^2=384$
$\Rightarrow\text{a}=\sqrt{\frac{384}{6}}=\sqrt{64}=8\text{ cm}$
$\therefore$ Volume $=\text{a}^2=8^3=512\text{ cm}^3$
View full question & answer→MCQ 291 Mark
If each side of a cube is doubled, its surface area:
- A
- ✓
Becomes $4$ times.
- C
Becomes $6$ times.
- D
Becomes $8$ times.
AnswerCorrect option: B. Becomes $4$ times.
Let side of cube in frist case $= a$
Then surface area $= 6a^2$
And side of second cube $= 2a$
Surface area $= 6(2a)^2= 6 \times 4a^2= 24a^2$
Ratio $=\frac{24\text{a}^2}{6\text{a}^2}=4$
Becomes $4$ times.
View full question & answer→MCQ 301 Mark
If the capacity of a cylindrical tank is $1848m^3$ and the diameter of its base is $14\ m,$ the depth of the tank is :
AnswerCapacity of cylindrical tank $= 1848m^3$
Diameter $= 14m$
$\therefore\text{Radius}(\text{r})=\frac{14}{2}=7\text{m}$
$\therefore\text{Depth}=\frac{\text{Volume}}{\pi\text{r}^2}=\frac{1848\times7}{22\times7\times7}$
$=\frac{264}{22}=12\text{m}$
View full question & answer→MCQ 311 Mark
Mark against the correct answer in the following: The length, breadth and height of a cuboid are in the ratio $3 : 4 : 6$ and its volume is $576\ cm^3$. The whole surface area of the cuboid is:
- A
$ 216 \mathrm{~cm}^2 $
- B
$ 324 \mathrm{~cm}^2 $
- ✓
$ 432 \mathrm{~cm}^2 $
- D
$ 460 \mathrm{~cm}^2 $
AnswerCorrect option: C. $ 432 \mathrm{~cm}^2 $
Volume $= lbh\ $
$ 3x \times 4x \times 6x = 72x^3= 576\ cm^3$
$\Rightarrow\text{x}=\sqrt[3]{\frac{576}{72}}=2$
$\therefore$ Total Surface area,
$= 2(lb + bh + lh) = 2(3x4x + 4x6x + 3x6x) $
$= 2(48 + 96 + 72) = 432\ cm^2$
View full question & answer→MCQ 321 Mark
Mark against the correct answer in the following: The circumference of the circular base of a cylinder is $44\ cm$ and its height is $15\ cm.$ The volume of the cylinder is:
- A
$ 1155 \mathrm{~cm}^3 $
- ✓
$ 2310 \mathrm{~cm}^3 $
- C
$ 770 \mathrm{~cm}^3 $
- D
$ 1540 \mathrm{~cm}^3 $
AnswerCorrect option: B. $ 2310 \mathrm{~cm}^3 $
Height $= 15\ cm$
Circumference $=2\pi\text{r}=44\text{ cm}$
$\therefore\text{r}=\frac{44\times7}{2\times22}=7\text{ cm}$
$\therefore$ Volume $=\pi\text{r}^2\text{h}=\frac{22}{7}\times7\times7\times15=2310\text{ cm}^3$
View full question & answer→MCQ 331 Mark
The volume of a cube is $343\ cm^3$. Its total surface area is :
- A
$196 \mathrm{~cm}^2$
- B
$49 \mathrm{~cm}^2$
- ✓
$294 \mathrm{~cm}^2$
- D
$147 \mathrm{~cm}^2$
AnswerCorrect option: C. $294 \mathrm{~cm}^2$
Volume of cube $= 343\ cm^2$
Side $=\sqrt[3]{343}=\sqrt[]{7\times7\times7}$
$= 7\ cm$
Total surface area $= 6(\text{side})^2$
$= 6 \times (7)^2$
$= 6 \times 49\ cm^2$
$= 294\ cm^2$
View full question & answer→MCQ 341 Mark
The area of the cardboard needed to make a box of size $25\ cm \times 15\ cm \times 8\ cm$ will be:
- A
$ 390 \mathrm{~cm}^2 $
- ✓
$ 1390 \mathrm{~cm}^2 $
- C
$ 2780 \mathrm{~cm}^2 $
- D
$ 1000 \mathrm{~cm}^2 $
AnswerCorrect option: B. $ 1390 \mathrm{~cm}^2 $
Size of box $= 25\ cm, 15\ cm, 8\ cm$
Surface area $= (lb + bh + hl)$
$ =2(25 \times 15+15 \times 8+8 \times 25) \mathrm{\ cm}^2 $
$ =2(375+120200) \mathrm{\ cm}^2 $
$ =2(695) $
$ =1390 \mathrm{~\ cm}^2 $
View full question & answer→MCQ 351 Mark
How many bricks, each measuring $25\ cm \times 11.25\ cm \times 6\ cm,$ will be needed to build a wall $8m$ long, $6m$ high and $22.5\ cm$ thick ?
- A
$5600$
- B
$6000$
- ✓
$6400$
- D
$7200$
AnswerCorrect option: C. $6400$
Length of wall $(l) = 8m = 800\ cm,$
Breadth $(b) = 22.5\ cm$
Height $(h) = 6m$
$= 600\ cm$
$\therefore$ Volume of wall $= l \times b \times h = 800 \times 22.5 \times 600\ cm^3$
$= 10800000\ cm^3$
Volume of bricks $= 25 \times 11.25 \times 6\ cm^3$
$= 1687.5\ cm^3$
$\therefore$ Number of bricks required,
$=\frac{10800000}{1687.5}=6400$
View full question & answer→MCQ 361 Mark
$66\ cm^3$ of silver is drawn into a wire $1\ mm$ in diameter. The length of the wire will be:
- A
$78m$
- ✓
$84m$
- C
$96m$
- D
$108m$
Answer Volume of silver $= 66\ cm^3$
Diameter of wire $1\ mm =\frac{1}{10}$
$\therefore$ Radius $=\frac{1}{20}\text{ cm}$
Then length $(h) =\frac{\text{Volume}}{\pi\text{r}^2}$
$=\frac{66\times7\times20\times20}{22\times1\times1}\text{ cm}$
$=8400\text{ cm}=84\text{ cm}$
View full question & answer→MCQ 371 Mark
The ratio of the radii of two cylinders is $2 : 3$ and the ratio of their heights is$5 : 3$. The ratio of their volumes will be
- A
$4 : 9$
- B
$9 : 4$
- ✓
$20 : 27$
- D
$27 : 30$
AnswerCorrect option: C. $20 : 27$
View full question & answer→MCQ 381 Mark
The diameter of a cylinder is 14 cm and its curved surface area is $220 cm^2$ the volume of the cylinder is
- ✓
$770 cm^3$
- B
$1000 cm^3$
- C
$1540 cm^3$
- D
$6622 cm^3$
AnswerCorrect option: A. $770 cm^3$
View full question & answer→MCQ 391 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. $396 cm^3$
View full question & answer→MCQ 401 Mark
The height of a cylinder is 80 cm and the diameter of its base is 7 cm. The whole surface area of the cylinder is
- ✓
$1837 cm^2$
- B
$1760 cm^2$
- C
$1942 cm^2$
- D
$3080 cm^2$
AnswerCorrect option: A. $1837 cm^2$
View full question & answer→MCQ 411 Mark
The height of a cylinder is 14 cm and its diameter is 10 cm. The volume of the cylinder is
- ✓
$1100 cm^3$
- B
$3300 cm^3$
- C
$3500 cm^3$
- D
$7700 cm^3$
AnswerCorrect option: A. $1100 cm^3$
View full question & answer→MCQ 421 Mark
$66 cm^3$ of silver is drawn into a wire 1 mm in diameter. The length of the wire will be
View full question & answer→MCQ 431 Mark
The number of coins, each of radius 0.75 cm and thickness 0.2 cm, to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is
AnswerD
Let the number of cotns be $n$. Then
$n \times \pi \times \frac{75}{100} \times \frac{75}{100} \times \frac{2}{10}=\pi \times 3\times 3 \times 8 \text {. Find } n$
View full question & answer→MCQ 441 Mark
The ratio of the total surface area to the lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is
- A
$2 : 1$
- B
$3 : 2$
- ✓
$4 : 3$
- D
$5 : 3$
AnswerCorrect option: C. $4 : 3$
View full question & answer→MCQ 451 Mark
If the capacity of a cylindrical tank is 1848 m³ and the diameter of its base is 14 m, the depth of the tank is
MCQ 461 Mark
A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?
- A
$32 m^3$
- B
$36 m^3$
- C
$40 m^3$
- ✓
$44 m^3$
AnswerCorrect option: D. $44 m^3$
View full question & answer→MCQ 471 Mark
Five equal cubes, each of edge 5 cm, are placed adjacent to each other. The volume of the cuboid so formed, is
- A
$125 cm^3$
- B
$375 cm^3$
- C
$525 cm^3$
- ✓
$625 cm^3$
AnswerCorrect option: D. $625 cm^3$
View full question & answer→MCQ 481 Mark
Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is
MCQ 491 Mark
If each side of a cube is doubled, its surface area
MCQ 501 Mark
If each side of a cube is doubled then its volume
AnswerD
$\sqrt{3} a = 9 \sqrt{3} \Rightarrow a = 9 cm$
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