Question

The diameter of a spherical balloon that is being filled with air is increasing at the rate of 3 inches more than the time, t. What will the volume, V, of the balloon be at t = 3 seconds

Answer 1

It is given that the diameter of the sphere increases at the rate of 3 inches more than the time, t. 
This means that:
at a certain time = t seconds
the diameter of the sphere will be equal to t + 3 

Based on this:
at t = 3 seconds
diameter of the sphere = t + 3 = 3 + 3 = 6 inches = 0.1524 meters
and radius of sphere = 0.5 x 0.1524 = 0.0762 meters

Volume of the sphere can be calculated using the following rule:
volume of sphere = (4/3) x pi x (radius)^3
Substituting in this equation, we can get the volume of the sphere at t = 3 seconds as follows:
volume at t=3 seconds = (4/3) x 3.14 x (0.0762)^3 = 1.8533 x 10^-3 m^3