# 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 rate at which the area is decreasing with respect to time when the radius is 4 feet?

1. 👍 0
2. 👎 0
3. 👁 2,018
1. V = (4/3)πr^3
dV/dt = 4πr^2 dr/dt
given dV/dt = 10 ft^3/min
so at r = 4
10 = 4π(16) dr/dt
dr/dt = 10/(64π) or appr. .05 ft/min

If A = 4πr^2, do the second question the same way.

1. 👍 1
2. 👎 0

## Similar Questions

1. ### math-calculus

A spherical party balloon is being inflated with helium pumped in at a rate of 12 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 1 ft?

2. ### Calculus - Rate of Change

Can someone explain how to solve this problem? Sand is being dumped on a conveyor belt onto a pile in such a way that the pile forms in the shape of a cone whose radius is always equal to its height. Assuming that the sand is

3. ### 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?

4. ### 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

1. ### Calculus

A balloon is rising vertically above a level, straight road at a constant rate of 1 foot/second. Just when the balloon is 65 feet above the ground, a bicycle passes under it going 17 feet/sec. How fast is the distance between the

2. ### Calculus

A spherical balloon is being inflated.Let r(t)=3t can represents its radius at time t seconds and let g(r)=4/3 pie r be the volume of the same balloon if its radius is r.Write (g.r) in terms of t and describe what it represents.

3. ### Calculus

A rectangular trough is 8 feet long, 2 feet aross the top and 4 feet deep, if water flows in At a rate of 2 cubic feet per minute. How fast is the surface rises when the water is 1 feet deep.?

4. ### 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?

1. ### Math

A swimming pool is 40 feet long, 20 feet wide, 8 feet deep at the deep end, and 3 feet deep at the shallow end; the bottom is rectangular. If the pool is filled by pumping water into it at the rate of 40 cubic feet per minute, how

2. ### 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? Note: The volume of a sphere is given by 4(pi)r^3

3. ### Calculus

A spherical balloon is inflated with gas at the rate of 20 cubic feet per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 1 foot and (b) 2 feet?

4. ### Calculus

A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2cm/min. At what rates are the volume and surface area of the balloon increasing when the radius is 5cm?