WBBSE Class 10 Maths Mensuration Chapter 1 Rectangular Parallelopiped Or Cuboid Multiple Choice Questions

WBBSE Class 10 Maths Mensuration Chapter 1 Rectangular Parallelopiped Or Cuboid Multiple Choice Questions

Example 1. The inner volume of a cuboidal box is 440 c.c. and the area of the inner base is 88 sq. The inner height is

1. 4 cm
2. 5 cm
3. 3 cm
4. 6 cm

Read And Learn Also WBBSE Class 10 Maths Multiple Choice Questions

Solution: base x height = volume

∴ height = \(\frac{440}{80}\) = 5

∴ The correct answer is 2. 5 cm

Example 2. The length, breadth and height of a cuboidal hole are 40 m, 12 m, and 16 m respectively. The number of planes having a height of 5 m, a breadth of 4 m and a thickness of 2 m can be kept in the hole is

1. 190
2. 192
3. 184
4. 180

Solution: Number of Planks = \(\frac{\text { volume of the hole }}{\text { volume of a plank }}=\frac{40 \times 12 \times 16}{5 \times 4 \times 2}=192\)

∴ The correct answer is 2. 192

Surface Areas And Volumes Mcqs Class 10

Example 3. The total surface area of a cube is 384 sq. m, the volume of the cube is

1. 64 cu.m
2. 216 cu.m
3. 256 cu.m
4. 512 cu.m

Solution: 6a² = 384

or, a² = \(\frac{384}{6}\) = 64

∴ a = 8

volume = 8³ cu.m = 512 cu. m

∴ The correct answer is 4. 512 cu.m

Example 4. The ratio of the volume of the two cubes is 1: 27, and the ratio of the total surface area is

1. 1: 3
2. 1: 8
3. 1: 7
4. 1: 9

Solution: Let the lengths be a₁, and a₂ units respectively

∴ \(\frac{a_1^3}{a_2^3}=\frac{1}{27}\)

⇒ or, \(\frac{a_1}{a_2}=\frac{1}{3}\)

⇒ or, \(\frac{4 a_1^2}{4 a_2^2}=\frac{4}{4}: \frac{1}{9}=1: 9\)

The correct answer is 4. 1: 9

Surface Areas And Volumes Mcqs Class 10

Example 5. If the total surface area of a cube is S sq. unit and the length of the diagonal is d unit, then the relation between S and d is

1. S = 6d²
2. 3S = 7d
3. S³ = d²
4. d² = \(\frac{S}{2}\)

Solution: 6a² = S, √3a = d

∴ \(6\left(\frac{d}{\sqrt{3}}\right)^2=\mathrm{S}\)

⇒ or, \(\frac{6 d^2}{3}=\mathrm{S}\)

⇒ or, 2d² = S

⇒ or, \(d^2=\frac{S}{2}\)

∴ The correct answer is 4. \(d^2=\frac{S}{2}\)

Example 6. If length of the diagonal of each surface of a cube is 8√2 cm, then the length of the diagonal of the cube is

1. 5√3 cm
2. 6√3 cm
3. 7√3 cm
4. 8√3 cm

Solution: side x √2 = 8√2 cm or, side = 8cm

⇒ Length of the diagonal = 8√3 cm

∴ The correct answer is 4. 8√3 cm

Example 7. Sum of the edges of a cube is 60 cm. Volume will be

1. 85 cu. cm
2. 110 cu. cm
3. 125 cu. cm
4. 100 cu. cm

Solution: 12a = 60, a = 5

∴ Volume = 5³ cu. cm = 125 cu. cm

∴ The correct answer is 3. 125 cu. cm

Class 10 Mensuration Chapter 1 Mcqs With Answers

Example 8. Length of a diagonal of a surface of a cuboid is \(\sqrt{a^2+b^2}\) unit and the height is c unit. Length of the diagonal of the cuboid is

1. \(\sqrt{a^2+b^2+c^2}\) unit
2. \(\sqrt{abc}\)
3. (a² + b² + c²) unit
4. abc unit

Solution: Length of the diagonal = \(\sqrt{\text { length }^2+(\text { breadth })^2+(\text { height })^2}\)

= \(\sqrt{a^2+b^2+c^2}\) unit

∴ The correct answer is 1. \(\sqrt{a^2+b^2+c^2}\) unit

Example 9. No of vertices, edges and surfaces of a cuboid are x, y, and z respectively. Then x – y + z =

1. 1
2. 2
3. 3
4. 4

Solution: x = 8, y = 12, z = 6

∴ x-y + z = 8-12 + 6 = 2

∴ The correct answer is 2. 2

Surface Areas And Volumes Mcqs With Solutions

Example 10. The length of the edges of a cubical tin pot is 30 cm. What maximum quantity of water in litres will it contain?

1. 27
2. 27000
3. 1000
4. None of these

Solution: Volume = (30 cm)³

= 27000 cu.cm = 27 litres

∴ The correct answer is 1. 27