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1. The sides of a rectangle are 8 cm and 6 cm. The corners of the rectangle lie on a circle. Find the are a of the circle without the rectangle :

A. 30.6 cm²

B. 39 cm²

C. 42.4 cm²

D. 65.3 cm²

Solution:

Diameter of the circle :

\begin{aligned} = A C = \sqrt{{(A B)}^{2} + {(B C)}^{2}} \\ = \sqrt{8^{2} + 6^{2}} \\ = \sqrt{100} c m \\ = 10 c m \end{aligned}

Radius = 5 cm
Required area = (Area of the circle) - (Area of the rectangle)
Area mcq solution image

\begin{aligned} = [(\frac{22}{7} \times 5 \times 5) - (8 \times 6)] c m^{2} \\ = (\frac{550}{7} - 48) c m^{2} \\ = (\frac{214}{7}) c m^{2} \\ = 30.57 c m^{2} \approx 30.6 c m^{2} \end{aligned}

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