# Calculus

posted by .

A spherical ball is being filled with air. When the radius r=9cm, the radius is increasing at a rate 4 cm/s. How fast is the volume changing at this time (leave your answer approximate)?

• Calculus -

V= 4/3 pi r^3
V= 4pi r^2 dt/dv
4= 4 pi (9)^2 dt/dv
1/81 pi

## Similar Questions

1. ### 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 …
2. ### 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 …
3. ### help on 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 …
4. ### 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?
5. ### Calculus

A tumor is assumed to be roughly spherical. If the radius R is found to be increasing at the rate of 0.5 mm/day when the radius is R=2 mm, how fast is the volume changing at this time?
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. ### Calculus

Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 cm^3 per second. How fast is the surface area of the balloon increasing when its radius is 9cm?
8. ### math

A spherical ball is being filled with air. When the radius r=7cm, the radius is increasing at a rate 2 cm/s. How fast is the volume changing at this time (leave your answer approximate)?
9. ### Calculus: need clarification to where the #'s go

Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 \mbox{cm}^3\mbox{/s}. How fast is the surface area of the balloon increasing when its radius is 14 \mbox{cm}?
10. ### Calculus

A spherical balloon is being inflated so that, at the time when the radius is 5m, the radius is increasing at the rate of 0.15m/s. (A) Find the rate of increase of the volume at this time. (B) If the rate of increase of volume thereafter …

More Similar Questions