Surface area of composite solids | Maths | Quizalize & Oak National Academy

Starter quiz

A circular cone is a 3D shape that has a circular base and one curved surface that narrows from the base to a fixed point called the ______.

'apex' ✓
This paper cup is cone-shaped. How many full paper cups of water can be poured into this cylindrical coffee mug?

2

2.5

3 ✓

3.5

4
The cone and cylinder share the same radius and vertical height. The volume of the cylinder is 1380 cm³. The volume of the cone is ______ cm³.

'460' ✓
Which calculation gives the volume of this cone?

$\frac{1}{3} \pi \times 16 \times 30$

$\frac{1}{3} \pi \times 16 \times 34$

$\frac{1}{3} \pi \times 16^2 \times 30$ ✓

$\frac{1}{3} \pi \times 8^2 \times 34$
The volume of this cone is ______ cm³ to the nearest cubic centimetre.

'8042' ✓
The volume of this cone is 768𝜋 cm³. The total surface area of the cone, in terms of 𝜋, is ______𝜋 cm²

'384' ✓

A __________ shape is a shape created using two or more basic shapes.

composite ✓

compound ✓

dual

multiple
This composite solid is constructed from two cuboids. All lengths given are in centimetres. Calculate the total surface area of the solid.

167 cm²

334 cm² ✓

344 cm²

354 cm²
This composite solid is constructed from two congruent cuboids. All lengths given are in centimetres. The total surface area of the solid is ______ cm².

'528' ✓
The composite solid is constructed by placing a hemisphere with diameter 10 cm on top of a cuboid. Find the surface area of the solid.

391 cm²

549 cm² ✓

627 cm²

706 cm²
The composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 10 cm. Find the surface area of the solid.

534 cm²

613 cm² ✓

770 cm²

848 cm²

927 cm²
The composite solid is constructed with a cone and a hemisphere. The surface area, in terms of 𝜋, is ______𝜋 cm².

'125' ✓

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The surface area of a composite solid is found by summing the area of all faces.
The faces may not always be the same shape.
The surface area may well be able to be calculated in a more efficient way.

Pupils may not subtract overlapping faces from their surface area calculation.

Ask the pupils to visualise turning around/rotating the compound solid, and consider which faces of the component solids would always be hidden.

Surface area - 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.
Solid - A solid is a shape that has three dimensions (e.g. width, height and depth).
Compound shape - A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.