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Volume Quiz - CBSE Class 6 Mathematics

Free practice quiz: Volume (CBSE Class 6 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 6 Mathematics practice quiz has 17 multiple-choice questions on Volume, and 17 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Volume of cuboids and cubes

Volume is the amount of space a solid takes up, measured in cubic units like cm³ or m³.
A cuboid's volume is length times breadth times height. A cube has all sides equal.
To find a cube's side from its volume, find the number that multiplied by itself three times gives the volume.

Cuboid

\[V = l \times b \times h\]

Cube

\[V = a^3\]

Side from volume

\[a = \sqrt[3]{V}\]

Common mistake: Adding the sides instead of multiplying them, or writing the answer in square units instead of cubic units.

Prisms and cylinders: base × height

Any solid with the same cross-section all along has volume equal to base area times height.
A cylinder's base is a circle, so its base area is πr².
If volume and base area are known, divide volume by base area to get height.

Prism

\[V = \text{Base area} \times h\]

Height from volume

\[h = \frac{V}{\text{Base area}}\]

Cylinder

\[V = \pi r^2 h\]

Radius from diameter

\[r = \frac{d}{2}\]

Common mistake: Using the diameter in place of the radius in πr². Always halve the diameter first.

Volume of cones and spheres

A cone holds one-third of what a cylinder with the same base and height holds.
A sphere's volume depends only on its radius, which is cubed in the formula.

Cone

\[V = \frac{1}{3}\pi r^2 h\]

Sphere

\[V = \frac{4}{3}\pi r^3\]

Common mistake: Forgetting the one-third for a cone, or squaring the radius instead of cubing it for a sphere.

Units of volume and capacity

Capacity tells how much liquid a container holds. It is measured in litres (L) and millilitres (mL).
One millilitre takes up the same space as one cubic centimetre.

mL and cm³

\[1\text{ mL} = 1\text{ cm}^3\]

Litre and mL

\[1\text{ L} = 1000\text{ mL}\]

Cubic metre and litres

\[1\text{ m}^3 = 1000\text{ L}\]

Common mistake: Mixing units, such as metres with centimetres. Convert all lengths to the same unit before multiplying.

Scaling dimensions changes volume

If every length is multiplied by k, the volume is multiplied by k × k × k.
This happens because volume uses three lengths multiplied together.

Scaled volume

\[V_{\text{new}} = k^3 \times V_{\text{old}}\]

Common mistake: Thinking the volume is multiplied by k only, when it is actually multiplied by k³.

Exam tips

Write the formula first, then substitute values, and always add cubic units to your answer.
Check whether the question gives the radius or the diameter before using any circle formula.
Use the value of π given in the question, and round only at the final step.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is the volume of a cube with side length 2 cm?
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Answer: B. 8 cm³
The volume of a cube is calculated using the formula V = side³. For a cube with side length 2 cm, the volume is 2³ = 8 cm³.
If the dimensions of a box are doubled, how does the volume change?
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Answer: C. It quadruples
If the dimensions of a box (length, width, and height) are doubled, the new volume becomes 2L × 2W × 2H = 8LWH, which is four times the original volume.
A cone has a radius of 3 cm and a height of 4 cm. What is its volume? (Use π ≈ 3.14)
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Answer: B. 37.68 cm³
The volume of a cone is V = (1/3)πr²h. For this cone, V = (1/3) × 3.14 × (3)² × 4 = 37.68 cm³.
A cylinder has a height of 10 cm and a base diameter of 8 cm. Calculate its volume. (Use π ≈ 3.14)
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Answer: A. 200.96 cm³
Volume of a cylinder is V = πr²h. The radius is 4 cm. Therefore, V = 3.14 × (4)² × 10 = 200.96 cm³.
If a pool is filled to a depth of 2 m, with a length of 8 m and a width of 5 m, what is the volume of water in cubic meters?
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Answer: A. 80 m³
Volume = length × width × height. Therefore, the pool can hold 8 m × 5 m × 2 m = 80 m³ of water.