Question

The radius of a sphere is decreased by $30\%$. What will be the percentage change in its total surface area?

Answer 1

Let $r$ be the radius of the original sphere.

Then the surface area of the original sphere is $4\pi r^2$.

If the radius of the sphere is decreased by $30\%$ then its radius will be $\frac{7r}{10}$.

Then the surface area of the new sphere will be $4\pi {\left(\frac{7r}{10}\right)}^2$$=4\pi r^2\times \frac{49}{100}$.

Now the surface area is decreased by $\frac{4\pi r^2-4\pi r^2\times \frac{49}{100}}{4\pi r^2}=\frac{51}{100}$.

So the percentage of the change in surface area is $51\%$.