# The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?

Let the diameter of a sphere be d.

After decreasing, diameter of the sphere
= d – $$\frac{25}{100}$$ x d
= d –$$\frac{1}{4} d = \frac{3}{4} d$$

Since, surface area of a sphere
= $$4\pi r^2$$
= $$\pi (2r)^2$$
= $$\pi d^2$$

Surface area of a sphere, when diameter of the sphere is

= $$\pi (\frac{3}{4} d)^2$$
= $$\pi \frac{9}{16} d^2$$

Now, decrease percentage in curved surface area
= $$\frac{\pi d^2 - \pi \frac{9}{16} d^2 }{\pi d^2} × 100$$
= $$\frac{16-9}{16} × 100$$
= $$\frac{7}{16} × 100$$
= 43.75%