A spherical balloon has a circumference of 10 inches. If it expands to twice the volume, what happens to its surface area?
A) Its surface area more than doubles.
B) Its surface area doubles.
C) Its surface area increases but does not double.

Question

Quizplus · Accepted Answer

The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$, and the surface area is $A = 4\pi r^2$. If the volume doubles, the new volume is $2V = \frac{8}{3}\pi r^3$, which means the radius increases by the cube root of 2. Since the surface area formula involves the square of the radius, the surface area increases by the square of the cube root of 2 ($\sqrt[3]{2}^2$), which is less than 2, meaning the surface area increases but does not double.

A Spherical Balloon Has a Circumference of 10 Inches