Question

Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second. How fast is the radius increasing after 2 minutes?

Answer 1

I would start with the equation for the volume of a sphere
\[ V = \frac{4}{3} \pi r^3 \]
take the derivative with respect to time:
\[ \frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt} \]

next, you need to find the volume of the balloon after being filled for 2 minutes (120 seconds)
use that to solve for r.

they tell you dV/dt = 3 cu ft/sec
you now have enough info to solve for dr/dt

Answer 2

3/1
proportion!
\[\frac{ 3 }{ 1 } \times60 \neq \frac{ 2 }{ x }\]
3 x 60
then multiply that by 2

Answer 3

or
3 x 120

Answer 4

360 cubic feet is my answer