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Year 11
Higher

Forming equations involving complex shape calculations

I can form and solve equations involving complex shapes and solids.

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New
New
Year 11
Higher

Forming equations involving complex shape calculations

I can form and solve equations involving complex shapes and solids.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

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

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.

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.

Encourage pupils to form and simplify the expressions for the volume or surface area for each 3D solid (or part of a compound 3D shape) before using these expressions to form and solve an equation. Encourage pupils to label each stage of their solution.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
A 3D shape that has 2 surfaces is a __________.
Correct answer: cone
cylinder
sphere
Q2.
The area of the curved surface of this frustum is 𝜋 cm². Leave your answer in terms of 𝜋.
An image in a quiz
Correct Answer: 216
Q3.
The total surface area of this frustum is 𝜋 cm². Leave your answer in terms of 𝜋.
An image in a quiz
Correct Answer: 396
Q4.
Work out the length of the side marked $$x$$ on this frustum.
An image in a quiz
Correct Answer: 20
Q5.
Find the area of the curved surface of this frustum. Leave your answer in terms of 𝜋.
An image in a quiz
420𝜋 cm²
440𝜋 cm²
460𝜋 cm²
Correct answer: 480𝜋 cm²
Q6.
The total surface area of this frustum is 𝜋 cm². Leave your answer in terms of 𝜋.
An image in a quiz
Correct Answer: 840

Exit quiz

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6 Questions

Q1.
Match each measurement to the correct formula.
Correct Answer:Surface area of hemisphere,$$3\pi r^2$$

$$3\pi r^2$$

Correct Answer:Surface area of cone ,$$\pi r l + \pi r^2$$

$$\pi r l + \pi r^2$$

Correct Answer:Surface area of cube ,$$6 l^2$$

$$6 l^2$$

Correct Answer:Surface area of sphere,$$2\pi r^2$$

$$2\pi r^2$$

Correct Answer:Surface area of cylinder ,$$2\pi r^2 + 2 \pi r h$$

$$2\pi r^2 + 2 \pi r h$$

Q2.
Select the algebraic expression for the volume of this cone.
An image in a quiz
$$81 \pi x$$
Correct answer: $$27 \pi x$$
$$9 \pi x^2$$
$$3\pi x^2$$
Q3.
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.
An image in a quiz
Correct Answer: 36
Q4.
Find the volume of a cube with a surface area of 294 cm².
64 cm³
125 cm³
216 cm³
Correct answer: 343 cm³
512 cm³
Q5.
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 $$r$$.
$$\frac {1}{3}\pi r^3$$
$$\frac {2}{3}\pi r^3$$
Correct answer: $$\pi r^3$$
$$\frac {4}{3}\pi r^3$$
Q6.
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.
Correct Answer: 150