# Calculus Homework

posted by .

You are blowing air into a spherical balloon at a rate of 7 cubic inches per second. The goal of this problem is to answer the following question: What is the rate of change of the surface area of the balloon at time t= 1 second, given that the balloon has a radius of 3 inches at that instant?

(a) Next write a formula relating the changing volume V(t) of the sphere to the changing radius r(t), and differentiate that formula with respect to t. Using what you know about V'(t) and r(1), find the rate of change of the radius at t=1 sec:

(b) Finally, write a formula relating the changing surface area S(t) of the sphere to the changing radius r(t), and differentiate that formula with respect to t. Use what you know about r(1) and r'(1) to determine the rate of change of the surface area at t=1 sec:

• Calculus Homework -

a = 4πr^2
da/dt = 8πr dr/dt

## 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. ### Calculus

A spherical balloon is being inflated at a rate of 10 cubic inches per second. How fast is the radius of the balloon increasing when the surface area of the balloon is 2pi square inches?
4. ### 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 …
5. ### 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 …
6. ### 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 …
7. ### calculus

A spherical balloon is being inflated at a rate of 10 cubic inches per second. How fast is the radius of the balloon increasing when the surface area of the balloon is square inches?
8. ### 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?
9. ### Calculus

A spherical water balloon is being filled with water at the rate of 125 cubic inches per minute. At what rate is the radius increasing when the radius is 10 inches?
10. ### calculus

is my answer to this question correct A spherical balloon is losing air at the rate of 2 cubic inches per minute. How fast is the radius of the ballon shrinking when the radius is 8 inches. Answer= .0024

More Similar Questions