# differential calculus

posted by .

Find how fast (a) the circumference (b)the area, if a cicle increases when the radius increases.

• differential calculus -

For absolute change rates:
dC/dt = 2*pi*dR/dt

dA/dt = 2*pi*R*dR/dt

For relative change rates
(1/C)dC/dt = (1/R) dR/dt

(1/A) dA/dt = (2/R)*dR/dt

## Similar Questions

1. ### calculus

Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm^3/s. How fast is the surface area of the balloon increasing when its radius is 7cm?
2. ### Calculus

Oil from a ruptured tanker spreads in a circular pattern. If the radius of the circle increases at the constant rate of 1.5 feet per second, how fast is the enclosed area increasing at the end of 2 hours?
3. ### Calculus

Oil from a ruptured tanker spreads in a circular pattern. If the radius of the circle increases at the constant rate of 1.5 feet per second, how fast is the enclosed area increasing at the end of 2 hours?
4. ### Calculus

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2m/s, how fast is the area of the spill increasing when the radius is 15m?
5. ### Calculus

A cicular metal plate is being heated and expands so that its radius increases at the rate of 0.25 mm/min. How fast is the area increasing when the radius is 10 cm?
6. ### 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?
7. ### calculus

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 3m/s, how fast is the area of the spill increasing when the radius is 15m?
8. ### math

using differential determine the appropriate increase in the surface area of a sphere if the radius increases from 4 cm to 4.05 cm.
9. ### Calculus

a cone has an altitude of 12 cm and a base radius which increases at the rate of 3 cm per minute. When the radius is 6 cm,how fast is the vertex angle increasing?
10. ### calculus

Water leaking onto a floor creates a circular pool with an area that increases at the rate of 3 square inches per minute. How fast is the radius of the pool increasing when the radius is 10 inches?

More Similar Questions