ABC26GN4625 · Area
Subject: General Aptitude · Chapter: Area · Exam: 2007 · Marks: · Difficulty:
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)$30.6 \mathrm{cm}^{2}$
(b)$39 \mathrm{cm}^{2}$
(c)$42.4 \mathrm{cm}^{2}$
(d)$65.3 \mathrm{cm}^{2}$
Answer
Explanation
Diameter of the circle $=A C=\sqrt{(A B)^{2}+(B C)^{2}}$ $$=\sqrt{8^{2}+6^{2}} \mathrm{cm}=\sqrt{100} \mathrm{cm}=10 \mathrm{cm} .$$ Radius $=5 \mathrm{cm}$. Required area = (Area of the circle) - (Area of the rectangle) $$\begin{aligned} & =\left[\left(\frac{22}{7} \times 5 \times 5\right)-(8 \times 6)\right] \mathrm{cm}^{2} \\ & =\left(\frac{550}{7}-48\right) \mathrm{cm}^{2}=\left(\frac{214}{7}\right) \mathrm{cm}^{2}=30.57 \mathrm{cm}^{2} \approx 30.6 \mathrm{cm}^{2} . \end{aligned}$$
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