A prism is a polyhedron with a base that is a polygon and a parallel opposite face that is identical. The corresponding edges of the two polygons are joined by parallelograms.

A cylinder is a 3D shape with a base that is a circle and a parallel opposite face that is identical. A cross-section of a cylinder made parallel to the base will be congruent to the base.

The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.

Volume is the amount of space occupied by a closed 3D shape.

Problem solving with further surface area and volume

Maths

In this unit, pupils have increased their knowledge of volume which is used in the compound measures unit as the formula for density involves volume. 

In the prior unit, pupils built upon their learning of the area of different shapes. In this unit, pupils will continue to further develop their understanding of shapes by considering surface area and volume of pyramids, spheres and cones.

2D and 3D shape: surface area and volume (pyramids, spheres and cones)

Name a 3D shape that has exactly one curved surface and no flat surfaces.

Starting with the cuboid with the smallest volume, put these cuboids into order of size according to their volumes.

Starting with the cuboid with the smallest surface area, put these cuboids into order of size according to their surface areas.

In this cuboid, the depth is $$k$$ cm. The lengths of the depth to the height to the width of the cuboid can be written in the ratio 1 : 2 : 4. Select an expression for the volume of the cuboid.

In this cuboid, the depth is $$k$$ cm. The lengths of the depth to the height to the width of the cuboid can be written in the ratio 1 : 2 : 4. Find an expression for the surface area of the cuboid.

A drink can contains 33 cl of sparkling water. The can has a radius of 4 cm. The height of the can is {{ }} cm to 1 d.p. (assume the can is a perfect cylinder and ignore the thickness of the metal).

The amount of space occupied by a closed 3D shape is called the __________ of the shape.

The diagram shows a composite solid constructed from two congruent cuboids. All lengths given are in centimetres. Which of these calculations give the total volume of the solid?

This composite solid is constructed from two cuboids. All lengths given are in millimetres. The total volume of the solid is {{ }} mm³.

This composite solid is constructed by placing a hemisphere with diameter 8 cm on top of a cuboid. Find the volume of the solid. Give your answer to the nearest cubic centimetre.

This composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 10 cm. The volume of the solid is {{ }}cm³ (correct to 4 significant figures).

This composite solid is constructed with a cone and a hemisphere. The volume of the solid, in terms of 𝜋, is {{ }}𝜋 cm³.

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