Question

Question 35

The area of a square is $100c{m}^2$. The circumference (in cm) of the largest circle cut of it is

(a) $5\pi$
(b) $10\pi$
(c) $15\pi$
(d) $20\pi$

Answer 1

Let the side of the square be 'a' cm.

Given area of square $=100c{m}^2$
$\therefore$ Area of square $=a^2$
$\Rightarrow a^2=100c{m}^2$ $[\because$ area of square $=(side{)}^2$]
$\Rightarrow a=\sqrt{100}$
$\Rightarrow a=10cm$
Now for the largest circle in the square, diameter of the circle must be equal to the side of square.
$\therefore$ Diameter = Side of a square = 10 cm
$\Rightarrow 2r=10cm$ $\because diameter=2\times radius]$
$\Rightarrow r=5cm$
$\therefore$ Circumference of the circle $=2\pi r=2\times \pi \times 5=10\pi cm$