## Exam-Style Questions on Similarity## Problems on Similarity adapted from questions set in previous exams. |

## 1. | GCSE Higher |

(a) Victor estimates the height of a flag pole by holding a ruler vertically so the height of the flag pole is exactly covered by the ruler when he is standing 240 centimetres from the flag pole.

The ruler is 30 cm long.

The horizontal distance of his eyes from the ruler is 40cm.

Calculate an estimate of the height of the flag pole.

(b) Give two reasons why this method may not be suitable to estimate the height of a very tall building.

## 2. | GCSE Higher |

(a) Find the area of a regular octagon if the distance from its centre to any vertex is 10cm.

(b) If the octagon had been cut from a piece of square card that was only just large enough, work out the area of the original square piece of card.

(c) A table top is made in the shape of a regular octagon with sides five times as long as the card model. Find the ratio of the area of the table top to the area of the card model.

## 3. | GCSE Higher |

Two similar pentagonal based pyramids have surface areas 200 cm^{2} and 50 cm^{2} respectively.

The volume of the larger pyramid is 800 cm^{3}.

Show that the volume of the smaller pyramid is 100 cm^{3}.

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