Mensuration MCQs

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Mensuration is responsible for dealing with concepts of lengths, areas and volumes, when it comes to two-dimensional and three-dimensional shapes. Mensuration defines principles of calculation and important equations and properties of geometric shapes and figures. Menstruation formula is applicable in solving real-life problems.

Ques 1. Find the area of a rhombus whose diagonals are given to be of lengths 6 cm and 7 cm.

30 cm²
21 cm²
28 cm²
42 cm²

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Answer: b) 21 cm²

Explanation: Since the area of a rhombus is given to be

Area = ½ X (product of lengths of the diagonals)

Therefore,

area = ½ X (6 X 7) cm²

= 21 cm²

Ques 2. Find the radius of a circle whose circumference is given to be 95 cm (take pi= 3.14).

18.32 cm
14.91 cm
15.13 cm
15.41 cm

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Answer: c) 15.13 cm

Explanation: We know that the circumference for a circle is given as,

C= 2πr

Substituting the values given in the question, we get

r = 95/ (2 X 3.14) cm

Hence, giving us,

r = 15.13 cm

Ques 3. Find the length of the edge of a cube whose surface area is given as 54 cm².

6 cm
9 cm
3 cm
12 cm

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Answer: c) 3 cm

Explanation: The surface area for a cube is given as

A = 6 (edge)².

Therefore, upon substituting the value for surface area in the above formula,

(edge)² = 54/ 6 cm²

= 9 cm²

After taking the square root, we get,

edge = 3 cm

Ques 4. What is the formula for the curved surface area of a regular cylinder?

πrh
πr²
πr²h
2πrh

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Answer: d) 2πrh

Explanation: The formula for the curved surface area of a regular cylinder is 2πrh

Ques 5. Find the breadth of a cuboid when the volume is given to be 64 m³ for length and height given as 8 m and 2 m, respectively.

8 m
2 m
4 m
6 m

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Answer: c) 4 m

Explanation: The volume for a cuboid is given as,

vol = length x breadth x height

Substituting the above-given values and rearranging the equation gives us

breadth = 64/ (8 x 2) m

= 4 m

Ques 6. Find the diameter of the circle whose area is given to be 113.04 m² (take pi = 3.14)

12 m
36 m
6 m
24 m

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Answer: a) 12m

Explanation: The area for a circle is known to be,

area= π r²

And the diameter for a circle is known to be,

d = 2 x r

Using the above two equations and substituting the values given in the question,

113.04 = 3.14 x r²

r² = 113.04/ 3.14 m²

r = 6 m

Hence,

d = 2 x r

Gives us,

d = 2 x 6 m

= 12 m

Ques 7. Find the area of a parallelogram with height and breadth given to be 11 cm and 12 cm, respectively.

66 cm²
132 cm²
144 cm²
121 cm²

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Answer: b) 132 cm²

Explanation: The formula for the area of a parallelogram is given as

area = base x height

Upon substituting the values for breadth and height, we get

area = 11 x 12 cm²

= 132 cm²

Ques 8. What is the area of a triangle whose base is given to be 7 cm and height as 8 cm?

56 cm²
28 cm²
23 cm²
21 cm²

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Answer: b) 28 cm²

Explanation: We know that the formula for the area of a triangle is,

area = ½ x base x height

Substituting the values for the base and height, we get,

area = ½ x 7 x 3 cm²

= 28 cm²

Ques 9. Find the height of a regular cylinder whose radius is 14 cm and the total surface area is 4342 cm² is (take pi= 22/7):

33.61 cm
29.45 cm
35.34 cm
39.41 cm

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Answer: d) 39.41

Explanation: For a given cylinder, we know that

Total surface area = 2πr (h + r)

Therefore,

4342= 2 x 22/7 x 14 (h + 14) cm²²

h = 35.34 cm

Ques 10. Find the perimeter of the largest circle that can fit inside a square with the side 7cm (take pi = 22/7).

14 cm
24 cm
28 cm
22 cm

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Answer: d) 22 cm

Explanation: Given, that the side of the square is 7cm

Hence, the diameter of the largest circle to fit inside the square, d = 7 cm

This implies that radius, r = 7/2 cm = 3.5 cm

Using the formula for circumference,

C = 2πr

We get,

C = 2 x 22/7 x 3.5 cm

= 22 cm

Ques 11. The number of pairs of identical faces in a cuboid.

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Answer: a) 3

Explanation: A cuboid comprises rectangles. Of the 6 faces, only 2 will be identical (i.e. present in pairs of l x b, b x h, h x l)

Ques 12. The area of a rhombus is 360 cm² and one of the diagonals is 12 cm. Find the other diagonal.

42 cm
60 cm
72 cm
54 cm

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Answer: b) 60 cm

Explanation: Because the area of a rhombus is given as,

area = ½ X (product of lengths of the diagonals)

Therefore, we get,

360 = ½ X (12 x diagonal²) cm²

diagonal² = 60 cm

Ques 13. A cuboidal box has its length, breadth and height given to be 10 cm, 5 cm and 15 cm, respectively. Find the total surface area for the cuboid

1000 cm²
600 cm²
550 cm²
800 cm²

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Answer: c) 550 cm²

Explanation: The formula for total surface area for a cuboid is given as

TSA = 2 x [(l × b) + (b × h) + (h × l)]

Hence, upon substituting the values for length, breadth and height,

TSA = 2 x [(10 x 5)+ (5 x 15) + (15 x 10)]

= 1300 cm²

Ques 14. Find the total surface area for a cube whose volume is given to be 512 m³.

384 cm²
644 cm²
586 cm²
822 cm²

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Answer: a) 384 cm²

Explanation: The volume for a cube is known to be

vol = edge x edge x edge

This implies,

512 = (edge)³. m³

Therefore,

edge = 8 m

Since, the total surface area for a cube is known to be

total surface area = 6 x (edge)²

Upon solving for the square root, we get,

TSA = 384 cm²

Ques 15. The area of a trapezium is 1240 m². The distance between the two pairs of parallel sides is given to be 20 m. If the length of one of the parallel sides is 60 m, find the length of the other parallel side.

68 m
54 m
64 m
70 m

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Answer: c) 64 m

Explanation: Using the formula for the area of a trapezium, we get

Area = ½ h (a+b)

Upon substituting the values given in the above question,

1240 = ½ x 20 x (60+b) m²

Solving the above equation for b gives us,

b = 64 m

Ques 16. 1litre = ______ cubic centimeters?

10 cm³
10000 cm³
100 cm³
1000 cm³

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Answer: d) 1000 cm³

Explanation: The conversion ratio from cubic meter to litres is

1 m³ = 1,000 l

Since 1 m³ = 1000000 cm³

Using the above two conversion ratios, we get

1 l = 1000 cm³

Ques 17. How many cubes with an edge length of 2 cm can fit inside a cuboid with dimensions of length, breadth and height given to be 8 m, 6 m, and 10 m, respectively?

60000
60000000
600000
6000

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Answer: b) 60000000

Explanation: Before we calculate the volume of the cuboid, we convert the length, breadth and height into mm from (using the conversion 1 m = 100 cm)

Therefore,

l = 800 cm

b = 600 cm

h = 1000 cm

Using the formula

vol = l x b x h

We get the volume of the cuboid as 480000000 cm³

The volume of one of the small cubes is 8 cm³(using the formula edge x edge x edge)

Hence, the total number of cubes that can fit inside the cuboid is calculated as

tot no. of cubes = 480000000/8

= 60000000

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Mensuration MCQs

CBSE X Related Questions

1.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

2.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

4.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

5.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

6.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

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Mensuration MCQs

CBSE X Related Questions

1.An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

2.The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

4.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

5.In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

6.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

2.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

4.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

5.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

6.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.