# Calculus Homework

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:

1. 👍
2. 👎
3. 👁
1. a = 4πr^2
da/dt = 8πr dr/dt

1. 👍
2. 👎

## 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? V= 4/3*pi*r^3 S= 4 pi r^2

2. ### Calculus

A spherical balloon is inflated at a rate of 10 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is 4 feet? And The radius of a circle is decreasing at a rate of 2 ft/minute. Find the

3. ### Math

A spherical balloon is to be deflated so that its radius decreases at a constant rate of 12 cm/min. At what rate must air be removed when the radius is 5 cm? Must be accurate to the 5th decimal place. It seems like an easy

4. ### Calculus

a spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. how fast is the radius of the balloon increasing at the instant the radius is 30 centimeters?

1. ### calculus

a spherical balloon filled with gas has a leak that permits the gas to escape at a rate of 1.5 cubic meters per minute. how fast is the surface area of the balloon shrinking when the radius is 4 meters?

2. ### UNM

In an air-conditioned room at 19.0C , a spherical balloon had the diameter of 50.0cm . When taken outside on a hot summer day, the balloon expanded to 51.0cm in diameter. What was the temperature outside? Assume that the balloon

3. ### math

The volume V of a sphere of radius r is given by the formula V (r) = (4/3)πr^3. A balloon in the shape of a sphere is being inflated with gas. Assume that the radius of the balloon is increasing at the constant rate of 2 inches

4. ### physics

an empty rubber balloon has mass 0.0120kg, the balloon is filled with helium of density 0.181 kg/m^3. the balloon is spherical w/ radius 0.500m. if the balloon is ties to a vertical string, what is thw tension in the string?

1. ### relaited rates

A spherical balloon is being inflated so that its volume is increasing at the rate of 5 cubic meter per minute.At what rate is the radius increasing when the radius is 6 meters?

2. ### 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? Enter your answer correct to 3 decimal

3. ### calculus

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.

4. ### Math

The radius r, in inches, of a spherical balloon is related to the volume V by r(V)= cubed√3V/4pi Air is pumped into the balloon so the volume after t seconds is given by V(t)=12+20t. a. Find the expression for the composite