# help on calculus

posted by .

A spherical balloon is being filled with air in such a way that its radius is increasing at a rate of 2 centimeters per second. At what rate is the volume of the balloon changing at the instant when its surface has an area of 4 pi or 12.56637061 square centimeters?

• help on calculus -

Volume = V = (4/3) pi r^3
dV/dt = 4 pi r^2 dr/dt
When the area 4 pi r^2 = 4 pi, the value of r is 1.

At that instant,
dV/dt = 4 pi *(1 cm^2)*2 cm/s
= 8 pi cm^3/s

• help on calculus -

Hhh

## Similar Questions

1. ### Calculus

Air is being pumped into a spherical balloon so that its volume increases at a rate of 30 cubic centimeters per second. How fast is the surface area of the balloon increasing when its radius is 19 cm?
2. ### calculus

Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 cubic centimeters per second. How fast is the surface area of the balloon increasing when its radius is 8 cm?
3. ### AP calculus AB

A spherical balloon is being filled with air in such a way that its radius is increasing at a rate of 2 centimeters per second. At what rate is the volume of the balloon changing at the instant when its surface has an area of 4 pi …
4. ### related rates problem-calculus

A spherical balloon is being filled with air in such a way that its radius is increasing at a rate of 2 centimeters per second. At what rate is the volume of the balloon changing at the instant when its surface has an area of 4 pi …
5. ### calculus

The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the volume changing when the radius is 8 centimeters?
6. ### Calculus

Air is being pumped into a spherical balloon and the volume is increasing at the rate of 100 cubic cm per minute. How fast is the radius of the balloon increasing when the radius is 10 cm?
7. ### Word Problem-Calculus

A spherical balloon is being inflated in such a way that its radius increases at a rate of 3 cm/min. If the volume of the balloon is 0 at time 0, at what rate is the volume increasing after 5 minutes?
8. ### calculus

air is being pumped into a spherical balloon at a rate of 8 cm^3/min. Find the rate at which the radius of the balloon is increasing when the balloon's radius is 5 cm.
9. ### math

Air is pumped into a balloon such that its volume increases at the rate of 75cm^3 per second. It is assumed that the balloon is spherical all the time. Find in term of pi the rate at which the radius of the balloon is increasing when …
10. ### Calculus

Air is being pumped into a spherical hot air balloon at a rate of 50 cm^3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 200 cm.

More Similar Questions