Pearson Edexcel IGCSE · Mathematics (Specification A)

Similarity: Practice Questions

4 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Similarity.

9 questions28 marksFree, no account

Question 1

1 mark

Two rectangles are mathematically similar. The smaller rectangle has a width of \(4\text{ cm}\) and a length of \(10\text{ cm}\). The larger rectangle has a width of \(6\text{ cm}\). Calculate the length of the larger rectangle.

Question 2

1 mark

Two triangles are mathematically similar. The ratio of their corresponding side lengths is \(2 : 5\). Given that the area of the smaller triangle is \(32\text{ cm}^2\), calculate the area of the larger triangle.

Question 3

1 mark

Two solid shapes are mathematically similar. The ratio of their surface areas is \(4 : 9\). Given that the volume of the larger solid is \(540\text{ cm}^3\), calculate the volume of the smaller solid.

Question 4

1 mark

Two mathematically similar solid ornaments have volumes of \(125\text{ cm}^3\) and \(216\text{ cm}^3\). The surface area of the smaller ornament is \(100\text{ cm}^2\). Calculate the surface area of the larger ornament.

Question 5

3 marks

Two mathematically similar triangles have corresponding sides in the ratio \(2:5\). If the area of the smaller triangle is \(16 \text{ cm}^2\), calculate the area of the larger triangle.

Write your answer out first, then check it against the worked solution.

Question 6

5 marks

Two mathematically similar containers have heights in the ratio \(2:3\). If the smaller container has a surface area of \(40 \text{ cm}^2\), find the surface area of the larger container.

Write your answer out first, then check it against the worked solution.

Question 7

6 marks

Two mathematically similar solid pyramids have volumes of \(432 \text{ cm}^3\) and \(2000 \text{ cm}^3\). Given that the surface area of the smaller pyramid is \(108 \text{ cm}^2\), calculate the surface area of the larger pyramid.

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Two solid cylinders, A and B, are mathematically similar.
The height of cylinder A is \( 10 \text{ cm} \) and the height of cylinder B is \( 15 \text{ cm} \).

(a) The surface area of cylinder A is \( 80 \text{ cm}^2 \). Calculate the surface area of cylinder B.

(b) The volume of cylinder B is \( 540 \text{ cm}^3 \). Calculate the volume of cylinder A.

Write your answer out first, then check it against the worked solution.

Question 9

5 marks

Two solid cylinders, A and B, are mathematically similar.
The volume of cylinder A is \(432\pi \text{ cm}^3\) and the volume of cylinder B is \(1024\pi \text{ cm}^3\).

(a) If the height of cylinder A is \(12 \text{ cm}\), calculate the height of cylinder B.

(b) The total surface area of cylinder B is \(640 \text{ cm}^2\). Calculate the total surface area of cylinder A.

Write your answer out first, then check it against the worked solution.

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

You've seen the model answer. Now get yours marked.

This page can show you how a good answer looks. It cannot tell you what your answer was missing. thinka marks your written work against the real mark scheme in about 15 seconds.

Get My Answers Marked Back to the notes

Want more questions like these? Get a fresh set on this topic, marked as you go.