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.

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.

The net of a 3D object is a 2D representation of its surfaces that can be folded up into the 3D object.

Checking and securing understanding of surface area of other prisms

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)

This prism has two congruent regular pentagonal faces and {{}} congruent rectangular faces.

Jun takes some measurements from a cube. Match each measurement to its correct value.

The surface area of this octagonal prism is {{ }} cm².

Dimensions of rectangle in the net: 8 cm by 80 cm

Dimensions of rectangle in the net: 8 cm by 300 cm

Total surface area = (300 + 5 × 80) cm²

Total surface area = (2 × 300 + 5 × (80 × 8)) cm²

Total surface area = (2 × 300 + 80 × 8) cm²

The diagram shows a prism unfolded into its net. The perimeter of the cross-sectional face is 80 cm. Which of these statements are correct?

The diagram shows the net of a triangular prism. The depth of the prism is 2 cm. The surface area of the prism that can be formed from this net is {{ }} cm². 

The cross-section of this prism is an equilateral triangle. The surface area of this triangular prism is {{ }} cm². Give your answer correct to 3 significant figures.

Select the units that could be used for the surface area of a cuboid.

(4 × 4) + (4 × 4) + (4 × 4) + (4 × 4) + (4 × 4) + (4 × 4)

Here is a net of a cube. Which calculations correctly give the surface area of the cube?

Here is a net of a cuboid. What is the surface area of the cuboid?

The diagram shows the plan view and front and side elevations of a cuboid. The surface area of the cuboid is {{ }}m².

The diagram shows an isometric drawing of a cuboid. The surface area of the cuboid is {{ }} m². 

Blue cuboid: width 2 cm, height 8 cm and length 16 cm

Red cuboid: width 4 cm, height 10 cm and length 10 cm

Yellow cuboid: width 6 cm, height 8 cm and length 10 cm

Purple cuboid: width 8 cm, height 8 cm and length 8 cm

Starting with the cuboid with the smallest surface area, put these cuboids in order of surface area size.

This lesson will be removed by end of Summer Term 2025.

Checking and securing understanding of surface area of other prisms

Lesson outcome

This lesson will be removed by end of Summer Term 2025.