Forming equations involving complex shape calculations | Maths

Starter quiz

A 3D shape that has 2 surfaces is a __________.

cone ✓

cylinder

sphere
The area of the curved surface of this frustum is ______𝜋 cm². Leave your answer in terms of 𝜋.

'216' ✓
The total surface area of this frustum is ______𝜋 cm². Leave your answer in terms of 𝜋.

'396' ✓
Work out the length of the side marked $x$ on this frustum.

'20' ✓
Find the area of the curved surface of this frustum. Leave your answer in terms of 𝜋.

420𝜋 cm²

440𝜋 cm²

460𝜋 cm²

480𝜋 cm² ✓
The total surface area of this frustum is ______𝜋 cm². Leave your answer in terms of 𝜋.

'840' ✓

Exit quiz

Match each measurement to the correct formula.

Surface area of hemisphere

⇔

$3\pi r^2$ ✓

Surface area of cone

⇔

$\pi r l + \pi r^2$ ✓

Surface area of cube

⇔

$6 l^2$ ✓

Surface area of sphere

⇔

$2\pi r^2$ ✓

Surface area of cylinder

⇔

$2\pi r^2 + 2 \pi r h$ ✓
Select the algebraic expression for the volume of this cone.

$81 \pi x$

$27 \pi x$ ✓

$9 \pi x^2$

$3\pi x^2$
The volume of this cone is the same as the volume of a sphere with a radius of 9 cm. The height, $x$ of the cone is ______ cm.

'36' ✓
Find the volume of a cube with a surface area of 294 cm².

64 cm³

125 cm³

216 cm³

343 cm³ ✓

512 cm³
The height of a cone is three times the length of its radius, $r$ . Find an algebraic expression for the volume of the cone in terms of $r$ .

$\frac {1}{3}\pi r^3$

$\frac {2}{3}\pi r^3$

$\pi r^3$ ✓

$\frac {4}{3}\pi r^3$
The radius of a cylinder is half of the height of the cylinder. The volume of the cylinder is 250𝜋 cm³. The surface area of the cylinder, in terms of 𝜋, is ______ cm².

'150' ✓

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Lesson Details

Key learning points

There are a variety of approaches to calculations involving shapes.
There are many skills you will need, such as algebraic manipulation and geometrical reasoning.
Displaced liquids can have their volumes calculated by finding the volume of the solid that displaced the liquid.

Common misconception

Pupils may only using given measures or terms in their calculations, even when these are not the lengths required to form an expression for the volume or surface area.

Encourage pupils to annotate diagrams to clearly show how the are breaking down a compound shape, and label clearly any new or missing lengths they can determine.

Keywords

Volume - The volume is the amount of space occupied by a closed 3D shape.
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.
Compound shape - A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.