# calculus

posted by .

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 80 mm?
mm^3/s

• calculus -

V = (4/3)*pi*r^3
dV/dt = 4*pi*r^2*(dr/dt)

In this case, dr/dt = 2 mm/s and
r = 80 mm

Do the calculation for dV/dt

• calculus -

12800pi

## Similar Questions

1. ### Pre-Calculus

As a balloon in the shape of a sphere is being blown up, the radius is increasing 1/pi inches per second. At what rate is the volume increasing when the radius is 1 inch?
2. ### college calculus

1) each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square is 16 cm^2?
3. ### calculus

Suppose that the radius r of a right circular cone of fixed height h = 20 cm is increasing at a rate 4 cm/s. How fast is the volume increasing when r = 10?
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

3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ). a. At the time when the radius of the sphere is 10 cm, what is the rate of increase …
6. ### Calculus

4. At time t, t>0, the volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t = 0, the radius of the sphere is 1 and at t = 15 the radius is 2. a. Find the radius of the sphere as a function …
7. ### calculus: related rates

hello, please help me. A cylindrical can is being heated with its height increasing at the rate of 0.01cm/min and its diameter at the rate of 0.005cm/min. At what rate is the volume increasing when the can has a diameter of 15cm and …
8. ### 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 …
9. ### Calculus- Related rates

A spherical balloon is inflated at the rate of 1 cm^3 per minuter. At the instant when the radius r=1.5, (a.) how fast is the radius increasing?
10. ### Calculus

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 100 mm?

More Similar Questions