Subject: General Aptitude · Chapter: Area · Exam: 2007 · Marks: · Difficulty:
The radius of a circle is 20\% more than the height of a right-angled triangle. The base of the triangle is 36 cm . If the area of triangle and circle be equal, what will be the area of circle?
(a)$72 \mathrm{cm}^{2}$
(b)$128 \mathrm{cm}^{2}$
(c)$144 \mathrm{cm}^{2}$
(d)$216 \mathrm{cm}^{2}$
(e)Cannot be determined
Answer
Answer (as printed): A
Explanation
Let the height of the triangle be $x \mathrm{cm}$. Then, radius of the circle $=(120 \%$ of $x) \mathrm{cm}=\left(\frac{6 x}{5}\right) \mathrm{cm}$. $$\therefore \quad \frac{1}{2} \times 36 \times x=\frac{22}{7} \times \frac{6 x}{5} \times \frac{6 x}{5} \Rightarrow x=\left(\frac{18 \times 7 \times 5 \times 5}{22 \times 6 \times 6}\right) \mathrm{cm} . \text { So, radius of the circle }=\left[\frac{6}{5} \times\left(\frac{18 \times 7 \times 5 \times 5}{22 \times 6 \times 6}\right)\right] \mathrm{cm}=\left(\frac{105}{22}\right) \mathrm{cm} .$$ ∴ $$\begin{aligned} \text { Area of the circle } & =\left(\frac{22}{7} \times \frac{105}{22} \times \frac{105}{22}\right) \mathrm{cm}^{2}=\left(\frac{1575}{22}\right) \mathrm{cm}^{2} \\ & =71.6 \mathrm{cm}^{2} \approx 72 \mathrm{cm}^{2} . \end{aligned}$$