NumericalModerate3 marks
In the given figure ABCD is a rectangle. It consists of a circle and two semi-circles each of which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to three significant figures.
Topic: Mensuration
Previous-year question practice database
Answer
Solution diagram
Exam answer
Rectangle: length = 20 cm, breadth = 10 cm.
Area of rectangle = 20 × 10 = 200 cm².
The circle and two semicircles all have radius 5 cm. Two semicircles together form one full circle.
Total circular area = 2πr² = 2 × 22/7 × 25 = 1100/7 ≈ 157.143 cm².
Shaded area = 200 − 157.143 ≈ 42.857 cm².
Correct to three significant figures:
Answer: 42.9 cm².
Explanation
Subtract one circle plus two semicircles from the area of the rectangle. The two semicircles together equal one full circle.
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