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Maths M.C.Q (1 Marks)

P-2 Mensuration · Maharashtra Board STD 10 (MSBSHSE - Semi English Medium). 38 questions.

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M.C.Q (1 Marks)

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38 questions · 34 auto-graded MCQ + 4 self-marked written.

Question 11 Mark
Choose the correct alternative answer for each of the following question.
Find the side of $a$ cube of volume $1 m^3.$
A. $1\ cm$
B. $10\ cm$
C. $100\ cm$
D. $1000\ cm$
 
Answer
Let the side of cube be $‘a’$ cm
Volume of cube, $V = a^3$
$\Rightarrow As 1m^3 = 10^6\ cm3$
$\Rightarrow a^3 = 10^6$
$\Rightarrow a = 100\ cm$
$\therefore $ Option $\text (B) $ is correct
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MCQ 21 Mark
Choose the correct alternative answer for each of the following question.
Find the volume of a cube of side $0.01\ cm.$
 
  • A
    $1 \ cm^3$
  • B
    $0.001 \ cm^3$
  • C
    $0.0001 \ cm^3$
  • ✓
    $0.000001 \ cm^3$
Answer
Correct option: D.
$0.000001 \ cm^3$
Side of the cube, $a = 0.01\ cm$
Volume of cube, $V = a^3$
$\Rightarrow V = (0.01)^3$
$\Rightarrow V = 0.000001 \ cm^3$​​​​​​​
$\therefore $ Option $(D)$ is correct
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Question 31 Mark
Choose the correct alternative answer for each of the following question.
A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is 5 cm, find the height of the cone.
A. 15 cm
B. 10 cm
C. 18 cm
D. 5 cm
Answer
Height of cylinder, $\mathrm{H}=5 \mathrm{~cm}$
Height of cone $=h$
Volume of cylinder, $V=\pi r^2 \mathrm{H}$
Volume of cone, $v=\frac{1}{3} \pi r^2 h$
Since cone is melted to form cylinder,
$\Rightarrow \mathrm{V}=\mathrm{v}$
$\Rightarrow H=\frac{h}{3}$
$\Rightarrow \mathrm{h}=3 \times \mathrm{H}$
$\Rightarrow \mathrm{h}=3 \times 5$
$\Rightarrow \mathrm{h}=15 \mathrm{~cm}$
$\therefore$ Option (A) is correct
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MCQ 41 Mark
Choose the correct alternative answer for each of the following question.
The curved surface area of a cylinder is $440 \mathrm{~cm}^2$ and its radius is $5 \ cm.$ Find its height.
  • ✓
    $44 / \pi \mathrm{cm}$
  • B
    $22 \pi \mathrm{cm}$
  • C
    $44 \pi \mathrm{cm}$
  • D
    $22 / \pi \mathrm{cm}$
Answer
Correct option: A.
$44 / \pi \mathrm{cm}$
Radius of cylinder, $r=5 \mathrm{~cm}$
Height of cylinder $=h$
Curved Surface Area of cylinder, $A=440 \mathrm{~cm}^2=2 \pi \mathrm{rh}$
$440=2 \times \pi \times 5 \times h$
$\Rightarrow h=\frac{44}{\pi}$
$\therefore$ Option $(A)$ is correct.
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MCQ 51 Mark
Choose the correct alternative answer for each of the following question.
Find the curved surface area of a cone of radius $7 \ cm$ and height $24 \ cm.$
  • A
    $440 \mathrm{~cm}^2$
  • ✓
    $550 \mathrm{~cm}^2$
  • C
    $330 \mathrm{~cm}^2$
  • D
    $110 \mathrm{~cm}^2$
Answer
Correct option: B.
$550 \mathrm{~cm}^2$
Radius, $r = 7\ cm$
Vertical Height, $h = 24 \ cm$
Slant Height, $l =\sqrt{ r ^2+ h ^2}$
$\Rightarrow l =\sqrt{7^2+24^2}$
$\Rightarrow l = 25 \ cm$
Curved Surface Area of cone, $A = \pi rl$
$\Rightarrow A=\frac{22}{7} \times 7 \times 25$
$\Rightarrow A = 550 sq.cm$
$\therefore$ Option $(B)$ is correct.
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Question 61 Mark
Choose the correct alternative answer for each of the following question.
Find the perimeter of a sector of a circle if its measure is 90° and radius is 7 cm.
A. 44 cm
B. 25 cm
C. 36 cm
D. 56 cm
Answer
Central angle, θ = 90°
Radius, r = 7cm
As we know that,
Length of arc, $l=\frac{\theta}{360} \times 2 \pi r$
$\Rightarrow l =\frac{90}{360} \times 2 \times \frac{22}{7} \times 7$
⇒ l = 11cm
Perimeter of sector =Length of sector + (2× Radius)
Perimeter = 11 + (2 × 7)
Perimeter = 25cm
∴ Option (B) is correct.
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Question 71 Mark
Choose the correct alternative answer for each of the following question.
If measure of an arc of a circle is 160° and its length is 44 cm, find the circumference of the circle.
A. 66 cm
B. 44 cm
C. 160 cm
D. 99 cm
Answer
Measure of arc, θ = 160°
Length of arc, l = 44cm
As we know that,
Length of arc, $l=\frac{\theta}{360} \times 2 \pi r$
$\Rightarrow 44=\frac{160}{360} \times \text { Circumference }$
⇒ Circumference = 99 cm
∴ Circumference of circle is 99cm, Option (D) is correct answer.
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MCQ 81 Mark
Choose the correct alternative answer for each of the following question.
The ratio of circumference and area of a circle is $2:7$. Find its circumference.
  • ✓
    $14 \pi$
  • B
    $7 / \pi$
  • C
    $7 \pi$
  • D
    $\frac{14}{\pi}$
Answer
Correct option: A.
$14 \pi$
Circumference of circle, $C=2 \pi r$
Area Of circle, $A=\pi r^2$
$\frac{\text { Circumference }}{\text { AArea }}=\frac{2}{7}$
$\Rightarrow \frac{2 \pi r}{\pi r^2}=\frac{2}{7}$
$\Rightarrow \mathrm{r}=7$
Circumference $=2 \times r \times \pi$
Circumference $=14 \pi$
$\therefore$ Option $(A)$ is correct
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MCQ 91 Mark
The volume of two spheres are in the ration 8 : 27, find the ratio of their radii.
  • ✓
    $2 : 3$
  • B
    $2 : 9$
  • C
    $1 : 3$
  • D
    $4 : 9$
Answer
Correct option: A.
$2 : 3$
$2 : 3$
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MCQ 101 Mark
Find the volume of a right circular cone if r = 14 cm and h = 9 cm.
  • A
    $161 cm^3$
  • B
    $2438 cm^3$
  • ✓
    $1848 cm^3$
  • D
    $1488 cm^3$
Answer
Correct option: C.
$1848 cm^3$
$1848 cm^3$
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MCQ 111 Mark
If the volume of cylinder is $12436 cm^3$ and radius and height of cylinder are in the ratio 2 : 3, find its height.
  • ✓
    21 cm
  • B
    7 cm
  • C
    14 cm
  • D
    18 cm
Answer
Correct option: A.
21 cm
21 cm
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MCQ 121 Mark
Bricks of dimensions $15 cm \times 8 cm \times 5cm$ are used to build a wall of dimensions $120 cm \times 16$ $cm \times 200 cm$. How many bricks are used?
  • A
    1280
  • ✓
    640
  • C
    160
  • D
    320
Answer
Correct option: B.
640
640
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MCQ 131 Mark
If $r=7 cm$ and $\theta=36^{\circ}$ then area of sector is _____ .
  • ✓
    $15.4 cm^2$
  • B
    $20.36 cm^2$
  • C
    $10.46 cm^2$
  • D
    $18.2 cm^2$
Answer
Correct option: A.
$15.4 cm^2$
$15.4 cm^2$
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MCQ 141 Mark
If $r=7 cm$ and $\theta=180^{\circ}$. Length of arc is _____ .
  • A
    44 cm
  • ✓
    22 cm
  • C
    10 cm
  • D
    18 cm
Answer
Correct option: B.
22 cm
22 cm
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MCQ 151 Mark
If diameter of a semicircle is 35 cm. Find its length.
  • A
    110 cm
  • ✓
    55 cm
  • C
    90 cm
  • D
    70 cm
Answer
Correct option: B.
55 cm
55 cm
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MCQ 161 Mark
A tent is made up of cylinder and mounted by a conical top. In order to calculate its total surface area, find sum of their.
  • A
    Volumes
  • B
    Total surface area
  • ✓
    Curved surface area
  • D
    Base areas
Answer
Correct option: C.
Curved surface area
Curved surface area
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MCQ 171 Mark
The length, breadth, height of cuboid are in the ratio $1 : 1 : 2,$ its total surface area is $1000\ cm^2$. Therefore  Its length is ________ .
  • ✓
    $10 \ cm$
  • B
    $15 \ cm$
  • C
    $20 \ cm$
  • D
    $12 \ cm$
Answer
Correct option: A.
$10 \ cm$
$10 \ cm$
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MCQ 181 Mark
Total surface area of a cube is $216 \ cm^2$​​​​​​​. Find its volume.
  • A
    $36 \ cm^3$
  • B
    $100 \ cm^3$
  • ✓
    $216 \ cm^3$
  • D
    $400 \ cm^3$
Answer
Correct option: C.
$216 \ cm^3$
$216 \ cm^3$
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MCQ 191 Mark
Vertical surface area of a cuboid is _______ .
  • A
    $2(l \times b)+h$
  • B
    $2(l \times b) \times h$
  • C
    $2(l+b)+h$
  • ✓
    $2(l+b) \times h$
Answer
Correct option: D.
$2(l+b) \times h$
$2(l+b) \times h$
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MCQ 221 Mark
A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is 5 cm, find the height of the cone.
Answer
Correct option: A.
A
Height of cylinder, $H =5 cm$
Height of cone $=h$
Volume of cylinder, $V=\pi r^2 H$
Volume of cone, $v=\frac{1}{3} \pi r^2 h$
Since cone is melted to form cylinder,
$\begin{array}{l}
\Rightarrow V=v \\
\Rightarrow H=\frac{h}{3} \\
\Rightarrow h=3 \times H \\
\Rightarrow h=3 \times 5 \\
\Rightarrow h=15 cm
\end{array}$
$\therefore$ Option $(A)$ is correct
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MCQ 231 Mark
The curved surface area of a cylinder is 440 cm2 and its radius is 5 cm. Find its height.
Answer
Correct option: A.
A
Radius of cylinder, $r=5 cm$
Height of cylinder $=h$
Curved Surface Area of cylinder, $A=440 cm ^2=2 \pi r h$
$\begin{array}{l}
440=2 \times \pi \times 5 \times h \\
\Rightarrow h=\frac{44}{\pi}
\end{array}$
$\therefore$ Option $(A)$ is correct.
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MCQ 241 Mark
Find the curved surface area of a cone of radius 7 cm and height 24 cm.
Answer
Correct option: B.
B
Radius, $r=7 cm$
Vertical Height, $h =24 cm$
Slant Height, $l=\sqrt{r^2+h^2}$
$\begin{array}{l}
\Rightarrow I=\sqrt{7^2+24^2} \\
\Rightarrow I=25 cm
\end{array}$
Curved Surface Area of cone, $A=\pi r l$
$\begin{array}{l}
\Rightarrow A=\frac{22}{7} \times 7 \times 25 \\
\Rightarrow A=550 \text { sq.cm }
\end{array}$
$\therefore$ Option (B) is correct.
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MCQ 251 Mark
Find the perimeter of a sector of a circle if its measure is 90° and radius is 7 cm.
Answer
Correct option: B.
B
Central angle, $\theta=90^{\circ}$
Radius, $r=7 cm$
As we know that,
$\begin{array}{l}
\text { Length of } \operatorname{arc}, 1=\frac{\theta}{360} \times 2 \pi r \\
\Rightarrow I=\frac{90}{360} \times 2 \times \frac{22}{7} \times 7 \\
\Rightarrow I=11 cm \\
\text { Perimeter of sector }=\text { Length of sector }+(2 \times \text { Radius }) \\
\text { Perimeter }=11+(2 \times 7) \\
\text { Perimeter }=25 cm
\end{array}$
$\therefore$ Option (B) is correct.
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MCQ 261 Mark
Answer
Correct option: D.
D
Measure of arc, $\theta=160^{\circ}$
Length of arc, $I=44 cm$
As we know that,
Length of $\operatorname{arc}, 1=\frac{\theta}{360} \times 2 \pi r$
$\Rightarrow 44=\frac{160}{360} \times$ Circumference
$\Rightarrow$ Circumference $=99 cm$
$\therefore$ Circumference of circle is $99 cm$, Option (D) is correct answer.
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MCQ 271 Mark
The ratio of circumference and area of a circle is 2:7. Find its circumference.
Answer
Correct option: A.
$14 \pi$
A
Circumference of circle, $C=2 \pi r$
Area Of circle, $A=\pi r^2$
$\begin{array}{l}
\frac{\text { Circumference }}{\text { Area }}=\frac{2}{7} \\
\Rightarrow \frac{2 \pi r}{\pi r ^2}=\frac{2}{7} \\
\Rightarrow r =7
\end{array}$
Circumference $=2 \times r \times \pi$
Circumference $=14 \pi$
$\therefore$ Option $(A)$ is correct
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MCQ 281 Mark
Vertical surface area of a cuboid is _______ .
  • A
    $2(l \times b)+h$
  • B
    $2(l \times b) \times h$
  • C
    $2(l+b)+h$
  • ✓
    $2(l+b) \times h$
Answer
Correct option: D.
$2(l+b) \times h$
D
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MCQ 291 Mark
Total surface area of a cube is 216 cm2. Find its volume.
  • A
    $36 cm^3$
  • B
    $100 cm^3$
  • ✓
    $216 cm^3$
  • D
    $400 cm^3$
Answer
Correct option: C.
$216 cm^3$
C
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MCQ 301 Mark
The volume of two spheres are in the ration 8 : 27, find the ratio of their radii.
  • ✓
    $2 : 3$
  • B
    $2 : 9$
  • C
    $1 : 3$
  • D
    $4 : 9$
Answer
Correct option: A.
$2 : 3$
A
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MCQ 311 Mark
The length, breadth, height of cuboid are in the ratio 1 : 1 : 2, its total surface area is 1000cm2. Therefore $\therefore$ Its length is ___ .
  • ✓
    10 cm
  • B
    15 cm
  • C
    20 cm
  • D
    12 cm
Answer
Correct option: A.
10 cm
A
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MCQ 321 Mark
If the volume of cylinder is $12436 cm^3$ and radius and height of cylinder are in the ratio 2 : 3, find its height.
  • ✓
    21 cm
  • B
    7 cm
  • C
    14 cm
  • D
    18 cm
Answer
Correct option: A.
21 cm
A
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MCQ 331 Mark
If $r=7 cm$ and $\theta=36^{\circ}$ then area of sector is _____ .
  • ✓
    $15.4 cm^2$
  • B
    $20.36 cm^2$
  • C
    $10.46 cm^2$
  • D
    $18.2 cm^2$
Answer
Correct option: A.
$15.4 cm^2$
A
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MCQ 341 Mark
If $r=7 cm$ and $\theta=180^{\circ}$. Length of arc is _____ .
  • A
    44 cm
  • ✓
    22 cm
  • C
    10 cm
  • D
    18 cm
Answer
Correct option: B.
22 cm
B
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MCQ 351 Mark
If diameter of a semicircle is 35 cm. Find its length.
  • A
    110 cm
  • ✓
    55 cm
  • C
    90 cm
  • D
    70 cm
Answer
Correct option: B.
55 cm
B
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MCQ 361 Mark
Find the volume of a right circular cone if r = 14 cm and h = 9 cm.
  • A
    $161 cm^3$
  • B
    $2438 cm^3$
  • ✓
    $1848 cm^3$
  • D
    $1488 cm^3$
Answer
Correct option: C.
$1848 cm^3$
C
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MCQ 371 Mark
Bricks of dimensions $15 cm \times 8 cm \times 5cm$ are used to build a wall of dimensions $120 cm \times 16$ $cm \times 200 cm$. How many bricks are used?
  • A
    1280
  • ✓
    640
  • C
    160
  • D
    320
Answer
Correct option: B.
640
B
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MCQ 381 Mark
A tent is made up of cylinder and mounted by a conical top. In order to calculate its total surface area, find sum of their.
  • A
    Volumes
  • B
    Total surface area
  • ✓
    Curved surface area
  • D
    Base areas
Answer
Correct option: C.
Curved surface area
C
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