Question

Three coins of the same size (radius $1cm$) are placed on table such that each of them touches the other two. The area enclosed by the coins is:

• A. $(\frac{\pi }{2}-\sqrt{3}){cm}^2$
• B. $(\sqrt{3}-\frac{\pi }{2}){cm}^2$
• C. $(2\sqrt{3}-\frac{\pi }{2}){cm}^2$
• D. $(3\sqrt{3}-\frac{\pi }{2}){cm}^2$

Answer 1

Answer: (B)

$(\sqrt{3}-\frac{\pi }{2}){cm}^2$

Radius of each coin $=1cm$

With all the three centres an equilateral triangle of side 2 cm is formed.

Area enclosed by coind $=$ Area of equilateral triangle $-3\times$ Area of sector of angle ${60}^o$

$=\frac{\sqrt{3}}{2}(2{)}^2-3\times \frac{60}{360}\times \pi (1{)}^2$

$=\frac{\sqrt{3}}{4}\times 4-3\times \frac{1}{6}\times \pi$

$=(\sqrt{3}-\frac{\pi }{2})c{m}^2$