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23 votes
23 votes
A circle with centre O has a radius of 6.2 cm.

AB is a diameter of the circle.
ABCD is a square.
Calculate the area of the shaded region.
You must show all your working.

A circle with centre O has a radius of 6.2 cm. AB is a diameter of the circle. ABCD-example-1
User Eyup
by
2.3k points

2 Answers

14 votes
14 votes

Answer:

it could either be 10.781 or 65.6, if not either of em then iam truly very sorry

Explanation:

User Arijit Mukherjee
by
3.2k points
17 votes
17 votes

The area of the shaded region is 81.14 cm^2.

Since AB is a diameter of the circle, the length of AB is equal to twice the radius of the circle, which is 2 * 6.2 cm = 12.4 cm.

Since ABCD is a square, the side length of the square is equal to half the length of AB, which is 12.4 cm / 2 = 6.2 cm.

The area of the square is equal to the side length squared, which is 6.2 cm * 6.2 cm = 38.44 cm^2.

The area of the circle is equal to pi * radius squared, which is 3.14 * 6.2 cm * 6.2 cm = 119.58 cm^2.

The area of the shaded region is equal to the area of the circle minus the area of the square, which is 119.58 cm^2 - 38.44 cm^2 = 81.14 cm^2.

Working:

Area of circle = pi * radius^2

= 3.14 * 6.2^2

= 119.58 cm^2

Area of square = side length^2

= 6.2^2

= 38.44 cm^2

Area of shaded region = area of circle - area of square

= 119.58 cm^2 - 38.44 cm^2

= 81.14 cm^2

Therefore, the area of the shaded region is 81.14 cm^2.

User OneNiceFriend
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2.9k points