Question

The radius of a sphere is increased by 10%, then

by what percent its surface area increases​

Answer 1

Answer:

21% increase in surface area

Step-by-step explanation:

The surface area of a sphere is $4\pi r^{2}$. Let the radius (r) of the initial sphere be 1. This makes the surface area of that sphere $4\pi$. If we increase the radius by 10% to 1.1, then the surface area is $4\pi (1.1)^{2}$, or $4.84\pi$. First, find the difference between the new sphere and initial one. Secondly, divide this value by the surface area of the initial, and finally, multiply by 100% to find the increase in surface area:

(($4.84\pi -4\pi$)/($4\pi$))(100%)=21%