Question

On decreasing the radius of a circle by 30 %, its area is decreased by

(a) 30 % (b) 60 % (c) 45% (d) none of these

Answer 1

Let the radius of the circle be r cm

So, area of the circle = $\pi$$r^2$

Now, radius decrease by 30%

So, the new radius = 0.7r

Area of the circle with new radius = $\pi$$(0.7r{)}^2$ = 0.49$r^2$$\pi$

Change in the area = $\pi$$r^2$ - 0.49$r^2$$\times$$\pi$

= 0.51$r^2$ $\times$$\pi$

% change in area = $\frac{0.51\times r^2\times \pi }{r^2\times \pi }$ $\times$ 100%
= 51%
Hence, the correct option is (d).