4MA1/2HR Jun 2022, Question 5: Composite Perimeter, Area and Volume
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
A square ABCD of area 36 cm² has four identical semicircles drawn outward on its sides as diameters. Calculate the total area of the whole shape, giving the answer to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 136 = 6 × 6 so side length is 6 cm
- 2radius of each semicircle = 6 ÷ 2 = 3 cm
- 3area of one full circle = π × 3² = 9π
- 4area of one semicircle = 9π ÷ 2 = 4.5π
- 54 semicircles = 4 × 4.5π = 18π
- 618π ≈ 56.5487
- 7total area = area of square + area of 4 semicircles = 36 + 56.5487 = 92.5487
- 892.5487 ≈ 92.5
Answer92.5
Stuck on a step? Read the free lesson: Composite Perimeter, Area and Volume
Practise more composite perimeter, area and volume questions
Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on composite perimeter, area and volume
Also searched as: 4MA1 2HR June 2022 · 4MA1/2HR · 4ma1 jun22 2hr · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.