Volume & surface area

18A cube has a volume of 512 cm³ Work out the surface area of the cube.

The diagram shows a solid shape made from a cylinder and a cone.

The cone has a base radius of 8 cm. The cylinder has a radius of 8 cm. The vertical height of the cone is three times the height of the cylinder. The volume of the solid shape is 640πcm³ Work out the vertical height of the cone. You must show all your working.

Here is a cuboid of length 10 cm and width 4 cm.

The cuboid has a volume of 200 cm³

Work out the height of the cuboid.

Here is a different cuboid.

Work out the total surface area of this cuboid.

Here are two cuboids.

All lengths are measured in centimetres. The volume of cuboid A is 142 cm³ greater than the volume of cuboid B. Work out the value of x.

The diagram shows a solid cylinder with base radius 3 cm and height 10 cm.

The cylinder is made from steel. It has a mass of 2250 g. Work out the density of the steel. Give your answer correct to 3 significant figures.

The diagram shows a solid cylinder with base radius 3 cm and height 8 cm. It also shows a solid cube with side length hcm.

The cylinder is made from steel with a density of 7.86 g/cm³ The cube is made from brass with a density of 8.5 g/cm³ The mass of the cylinder is equal to the mass of the cube. Work out the value of h. Give your answer correct to 1 decimal place.

The diagram shows a crate and a box.

The crate is 3 m by 1 m by 1.5 m. The crate is completely filled with boxes. Each box is 20 cm by 10 cm by 75 cm. Work out the number of boxes in the crate.

21A solid cuboid has a volume of 300 cm³ The cuboid has a total surface area of 370 cm² The length of the cuboid is 20 cm. The width of the cuboid is greater than the height of the cuboid. Work out the height of the cuboid. You must show all your working.

A paddling pool is in the shape of a cylinder.

The pool has radius 100 cm. The pool has depth 30 cm. The pool is empty. It is then filled with water at a rate of 250 cm³ per second. Work out the number of minutes it takes to fill the pool completely. Give your answer correct to the nearest minute. You must show all your working.

A paddling pool is in the shape of a cylinder.

The pool has radius 100 cm. The pool has depth 30 cm. The pool is empty. It is then filled with water at a rate of 250 cm³ per second. Work out the number of minutes it takes to fill the pool completely. Give your answer correct to the nearest minute. You must show all your working.

The diagram shows a cube and a square-based pyramid.

The volume of the cube is equal to the volume of the pyramid. Work out the perpendicular height, hcm, of the pyramid.

The diagram shows an empty tank in the shape of a cylinder.

The cylinder has radius 15 cm and height 43 cm. Water flows into the tank at a rate of 0.47 litres per minute. Calculate the number of minutes it will take to completely fill the tank. Give your answer correct to the nearest minute.

The diagram shows an empty tank in the shape of a cylinder.

The cylinder has radius 15 cm and height 43 cm. Water flows into the tank at a rate of 0.47 litres per minute. Calculate the number of minutes it will take to completely fill the tank. Give your answer correct to the nearest minute.

The front elevation of a cuboid is shown on the centimetre grid below.

The volume of the cuboid is 224 cm³ On the grid, draw the plan of the cuboid.

22A cube has a total surface area of 150 cm² Work out the volume of the cube.

The diagram shows a solid cylinder on a horizontal floor.

The cylinder has a volume of 1200 cm³ height of 40 cm. The cylinder exerts a force of 90 newtons on the floor. Work out the pressure on the floor due to the cylinder.

A cube has a total surface area of 150 cm² Work out the volume of the cube.

The diagram shows a solid cylinder on a horizontal floor.

The cylinder has a volume of 1200 cm³ height of 40 cm. The cylinder exerts a force of 90 newtons on the floor. Work out the pressure on the floor due to the cylinder.

Packets of sweets are put into boxes.

Packet Box Each packet is a cuboid, 80 mm by 60 mm by 20 mm. Each box is a cuboid, 72 cm by 48 cm by 24 cm. Work out the greatest number of packets that can be put into each box.

The diagram shows two similar solid triangular prisms, A and B.

The volume of prism A is 58.806 cm³ The volume of prism B is 1587.762 cm³ The cross section of each prism is a right-angled triangle. For prism B the length of the base of the triangle is 8.1 cm the area of the triangle is 43.74 cm² The height of the triangle for prism A is hcm. Work out the value of h.

Here is a cuboid.

Work out the volume of the cuboid.

Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80 cm and height 160 cm.

The 4 tanks are to be filled completely with a mixture of fertiliser and water. The fertiliser has to be mixed with water in the ratio 1: 100 by volume. Karina has 32 litres of fertiliser. 1 litre = 1000 cm³ Has Karina enough fertiliser for the 4 tanks? You must show how you get your answer.

Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80 cm and height 160 cm.

The 4 tanks are to be filled completely with a mixture of fertiliser and water. The fertiliser has to be mixed with water in the ratio 1: 100 by volume. Karina has 32 litres of fertiliser. 1 litre = 1000 cm³ Has Karina enough fertiliser for the 4 tanks? You must show how you get your answer.

The centimetre grid shows the plan and the front elevation of a cylinder.

Work out the volume of the cylinder. Give your answer in terms of π

Here are two cubes, A and B.

Cube A has a mass of 81 g. Cube B has a mass of 128 g. Work out the density of cube A: the density of cube B Give your answer in the form a: b, where a and b are integers.

The diagram shows a prism.

The cross section of the prism is a right‑angled triangle. The base of the triangle has length 5 cm The prism has length 25 cm The prism has volume 750 cm³ Work out the height of the prism.

The diagram shows a prism.

The cross section of the prism is a right‑angled triangle. The base of the triangle has length 5 cm The prism has length 25 cm The prism has volume 750 cm³ Work out the height of the prism.

27The diagram shows a prism placed on a horizontal floor.

The prism has height 3 m The volume of the prism is 18 m³ The pressure on the floor due to the prism is 75 newtons/m² Work out the force exerted by the prism on the floor.

The diagram shows a prism placed on a horizontal floor.

The prism has height 3 m The volume of the prism is 18 m³ The pressure on the floor due to the prism is 75 newtons/m² Work out the force exerted by the prism on the floor.

Here is a cuboid.

Work out the volume of the cuboid.

29The diagram shows a solid triangular prism.

The prism is made from wood with a density of 0.8 g/cm³ Work out the mass of this prism.

The diagram shows a prism.

The cross section of the prism has exactly one line of symmetry. Work out the volume of the prism. Give your answer correct to 3 significant figures.

Liquid A and liquid B are mixed together in the ratio 2: 13 by volume to make liquid C.

Liquid A has density 1.21 g/cm³ Liquid B has density 1.02 g/cm³

A cylindrical container is filled completely with liquid C. The cylinder has radius 3 cm and height 25 cm.

Work out the mass of the liquid in the container. Give your answer correct to 3 significant figures. You must show all your working.

A container is in the shape of a cuboid.

The container is full of water. A cup holds 275 ml of water. What is the greatest number of cups that can be completely filled with water from the container?

A container is in the shape of a cuboid.

The container is full of water. A cup holds 275 ml of water. What is the greatest number of cups that can be completely filled with water from the container?

The diagram shows a solid metal cuboid.

The areas of three of the faces are marked on the diagram. The lengths, in cm, of the edges of the cuboid are whole numbers.

The metal cuboid is melted and made into cubes. Each of the cubes has sides of length 2.5 cm.

Work out the greatest number of these cubes that can be made.

Here is a triangular prism.

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

The total surface area of a cube is 294 cm².

Work out the volume of the cube.

Chloe has a van.

She is going to use the van to deliver boxes. Each box is a cuboid, 40 cm by 30 cm by 35 cm.

The space for boxes in the van has maximum length 2.4 m maximum width 1.5 m maximum height 1.4 m

The space for boxes is empty. Chloe wants to put as many boxes as possible into the van.

She can put 3 boxes into the van in one minute. Assume that the space for boxes is in the shape of a cuboid.

Work out how many minutes it should take Chloe to put as many boxes as possible into the van.

The space for boxes might not be in the shape of a cuboid.

Explain how this could affect the time it would take Chloe to put as many boxes as possible into the van.

The diagram shows a cube of side length 2 cm.

Vera says,

“The volume of any solid made with 6 of these cubes is 48 cm³ ”

Is Vera correct? You must show your working.

Draw a cuboid that can be made with 6 of these cubes. Write the dimensions of the cuboid on your diagram.

Work out the surface area of your cuboid.