iGCSE Mathematics (0580) :E4.4 Calculate lengths of similar figures iGCSE Style Questions Paper 2

Question

The diagram shows three shapes that are mathematically similar.
The heights of the shapes are in the ratio small : medium : large = 1 : 5 : 8.

Find the ratio shaded area : total unshaded area. Give your answer in its simplest form.

▶️ Answer/Explanation

Solution

Ans: 3:5

1. Area ratio is square of height ratio: 1:25:64

2. Shaded area = medium – small = 25-1 = 24

3. Unshaded areas = small + (large – medium) = 1 + (64-25) = 40

4. Ratio shaded:unshaded = 24:40 = 3:5

Question

Similar triangles ABC and PQR

Triangle ABC is mathematically similar to triangle PQR. Find the value of x.

Two similar bowls

The diagram shows two mathematically similar bowls. The larger bowl has capacity 7.8 litres and height 11.5 cm. The smaller bowl has capacity 4 litres. Calculate the height of the smaller bowl.

▶️ Answer/Explanation

Answer:

(a) 1.84 (For similar triangles, corresponding sides are proportional.)

(b) 9.20 cm (For similar 3D shapes, heights scale with the cube root of volume ratios: \(11.5 \times \sqrt[3]{\frac{4}{7.8}}\).)

iGCSE Mathematics (0580) :E4.4 Calculate lengths of similar figures iGCSE Style Questions Paper 2

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