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

`V=36 \pi` cubic inches

Explanation:

Diameter is increasing at 3 inches more than time, When t = 3

Diameter (d) = 3+3 = 6

d = 6

Radius is HALF of diameter, so

r = 6/2 = 3

Now, the volume of a sphere is given by the formula:

`V=(4)/(3)\pi r^3`

Putting r = 3, we get:

`V=(4)/(3)\pi r^3\\V=(4)/(3)\pi (3)^3\\V=36 \pi`

The volume would be 36π