Question

A circle is inscribed in a square of side 10 cm. Find the area of the region between the square and the circle.

• A. 25(4 - π) cm²
• B. 25(π - 2) cm²
• C. 50(4 - π) cm²
• D. 50(π - 2) cm²

Answer 1

Answer: (A)

25(4 - π) cm²

Answer 2

The diameter of the circle is equal to the side of the square.

Diameter = 10 cm
$r = \frac{\text{Diameter}}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm}$
$\text{Area of circle} = \pi r^2 = \pi \times 5^2 = 25\pi \text{ cm}^2$

Area of square = side² = 10² = 100 cm²
Area of the region between the square and the circle:
= Area of square - Area of circle = 100 cm² - 25π cm² = 25(4 - π) cm²