Volume & Surface Area Practice Questions

Question 1

4 marks

Do not use a calculator for this question.

A lunch box is in the shape of a cuboid.
It measures $12$ cm by $8$ cm by $5$ cm.

(a)

Work out the volume of the lunch box.

....................................................... $\text{cm}^3$

/ 2

(b)

Work out the total surface area of the lunch box.

....................................................... $\text{cm}^2$

/ 2

Question 2

3 marks

Do not use a calculator for this question.

A cuboid storage box has a rectangular base measuring $18$ cm by $12$ cm.
The volume of the box is $1080\text{ cm}^3$ .

(a)

Work out the height of the box.

....................................................... cm

/ 2

(b)

Write down the capacity of the box in litres.

....................................................... litres

/ 1

Question 3

5 marks

Do not use a calculator for this question.

Here is a prism. Its cross-section is a triangle with base $6$ cm and perpendicular height $4.5$ cm. The prism is $12$ cm long.

(a)

Work out the volume of the prism.

....................................................... $\text{cm}^3$

/ 3

(b)

A second prism has the same triangular cross-section as this prism.
The volume of the second prism is $337.5\text{ cm}^3$ .

Work out the length of the second prism.

....................................................... cm

/ 2

Question 4

5 marks

Do not use a calculator for this question.

Ellie packs boxes of tea into a crate.

Each box of tea is a cuboid measuring $20$ cm by $15$ cm by $10$ cm.

The inside of the crate is a cuboid measuring $60$ cm by $45$ cm by $40$ cm.

(a)

Work out the greatest number of boxes of tea that can be packed into one crate.

.......................................................

/ 3

(b)

Ellie has $100$ boxes of tea to pack.

Work out the number of crates she needs.

.......................................................

/ 2

Question 0

5 marks

You may use a calculator for this question.

A water butt is in the shape of a cylinder.
The cylinder has diameter $60$ cm and height $80$ cm.

(a)

Work out the volume of the water butt.
Give your answer correct to 3 significant figures.

....................................................... $\text{cm}^3$

/ 3

(b)

The water butt is completely full of water.
Joe fills watering cans from the water butt.
Each watering can holds $5$ litres of water.

Work out the greatest number of watering cans Joe can completely fill.

.......................................................

/ 2

Question 0

3 marks

Do not use a calculator for this question.

The volume of a cube is $512\text{ cm}^3$ .

Work out the total surface area of the cube.

....................................................... $\text{cm}^2$

/ 3

Question 0

5 marks

You may use a calculator for this question.

A hollow plastic ball has radius $6$ cm.

Volume of a sphere $= \frac{4}{3}\pi r^3$ Surface area of a sphere $= 4\pi r^2$

(a)

Work out the surface area of the ball.
Give your answer correct to 3 significant figures.

....................................................... $\text{cm}^2$

/ 2

(b)

Marcus says, “The ball can be completely filled with $1$ litre of water.”

Is Marcus correct?
You must show your working.

/ 3

Question 0

6 marks

Do not use a calculator for this question.

The diagram shows a solid made from a cuboid with a square-based pyramid on top.

The cuboid has a square base of side $6$ cm and a height of $10$ cm.
The pyramid has a base of side $6$ cm and a height of $4.5$ cm.

Volume of a pyramid $= \frac{1}{3} \times$ area of base $\times$ height

(a)

Work out the total volume of the solid.

....................................................... $\text{cm}^3$

/ 4

(b)

The pyramid is removed from the top of the cuboid and replaced by a cube of side $6$ cm.

Work out the increase in the volume of the solid.

....................................................... $\text{cm}^3$

/ 2

Question 0

6 marks

You may use a calculator for this question.

Here is a solid cone.

The radius of the base is $5$ cm, the vertical height is $12$ cm and the slant height is $13$ cm.

Volume of a cone $= \frac{1}{3}\pi r^2 h$ Curved surface area of a cone $= \pi r l$

(a)

Work out the volume of the cone.
Give your answer correct to 3 significant figures.

....................................................... $\text{cm}^3$

/ 3

(b)

Work out the total surface area of the cone.
Give your answer correct to 3 significant figures.

....................................................... $\text{cm}^2$

/ 3

Question 0

5 marks

You may use a calculator for this question.

A tank is in the shape of a cylinder with radius $40$ cm and height $90$ cm.

The tank is empty.
Water flows into the tank at a rate of $8$ litres per minute.

Ravi says, “It will take less than one hour to fill the tank completely.”

Is Ravi correct?
You must show your working.

$1$ litre $= 1000\text{ cm}^3$

/ 5

Number

Algebra

Ratio, Proportion & Rates of Change

Geometry & Measures

Probability

Statistics

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