Volume of prisms

A cuboid measures 6 cm by 4 cm by 3 cm.

Work out the volume of the cuboid.

State the units of your answer.

A cylinder has a radius of 5 cm and a height of 12 cm.

Work out the volume of the cylinder.

Give your answer correct to 3 significant figures.

The cross-section of a prism is a right-angled triangle with base 8 cm and height 5 cm.

The length of the prism is 12 cm.

Work out the volume of the prism.

A cylindrical tin has a diameter of 8 cm and a height of 10 cm.

Work out the volume of the tin.

Give your answer correct to 3 significant figures.

A water tank is a cuboid measuring 50 cm by 40 cm by 30 cm.

1. Work out the volume of the tank in cm³.
2. Work out the capacity of the tank in litres. (1 litre = 1000 cm³)

A cuboid has a volume of 180 cm³.

The base of the cuboid measures 6 cm by 5 cm.

Work out the height of the cuboid.

A cylindrical water butt has a radius of 25 cm and a height of 80 cm.

Work out the number of litres of water the water butt holds when it is full.

Give your answer to the nearest litre.

1 litre = 1000 cm³

The cross-section of a prism is a trapezium.

The parallel sides of the trapezium are 6 cm and 10 cm, and the perpendicular distance between them is 4 cm.

The length of the prism is 15 cm.

Work out the volume of the prism.

A fish tank is a cuboid 60 cm long, 25 cm wide and 30 cm high. It is filled with water to a depth of 20 cm.

The water is poured into cups. Each cup holds 250 cm³. How many cups can be filled completely?

The cross-section of a prism is a rectangle 10 cm by 6 cm with a smaller rectangle 4 cm by 3 cm cut out of one corner. The prism is 15 cm long.

Work out the volume of the prism.

A swimming pool is a cuboid 25 m long, 10 m wide and 1.6 m deep. It is filled at a rate of 20 m³ per hour.

How many hours does it take to fill the pool completely?

A water tank is a cuboid measuring 1.5 m by 0.8 m by 0.6 m.

The tank is empty. Dev fills the tank completely with water.

Water costs £1.25 for every 100 litres.

Work out the cost of the water needed to fill the tank.

1 m³ = 1000 litres

The cross-section of a prism is a right-angled triangle.

The hypotenuse of the triangle is 13 cm and one of the shorter sides is 5 cm.

The length of the prism is 20 cm.

Work out the volume of the prism.

A cuboid has a length of 8 cm and a width of 5 cm. Its volume is 280 cm³.

1. Work out the height of the cuboid.
2. Work out the total surface area of the cuboid.

A cylindrical tank has a radius of 30 cm and a height of 80 cm. It is filled with water from a tap at 12 litres per minute.

How long does it take to fill the tank? Give your answer in minutes, to 1 decimal place. (1 litre = 1000 cm³)

A solid metal cube has sides of 6 cm. It is melted down and made into a cuboid with a square base of side 4 cm.

Work out the height of the cuboid.

A cylindrical tub has a radius of 12 cm and a height of 20 cm. It is filled with a mixture of squash and water. The squash and water are in the ratio 1 : 9 by volume.

How many millilitres of squash are needed? Give your answer to 3 significant figures. (1 cm³ = 1 ml)

The cross-section of a prism is an L-shape.

The L-shape is made by starting with a rectangle 12 cm wide and 9 cm tall, then removing a 7 cm by 5 cm rectangle from the top right corner.

The length of the prism is 24 cm.

Show that the volume of the prism is 1752 cm³.

A prism has a cross-section that is a right-angled triangle. The base of the triangle is 9 cm and the angle between the base and the hypotenuse is 35°. The prism is 12 cm long.

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