# 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 question but no matter how many times i attempt it I get it wrong.

1. 👍 0
2. 👎 0
3. 👁 1,058
1. Most questions of this type appear to disregard pressure, so in the following solution I will do the same (physics expert will surely groan)

V = (4/3)π r^3
dV/dt = 4πr^2 dr/dt

so when r = 5 and dr/dt = -12

dV/dt = 4π(25)(-12)
= appr -3769.91118

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Mathematics

A spherical balloon is being inflated. Given that the volume of a sphere in terms of its radius is v(r)=(4/3)(pi(r^3)) and the surface area of a sphere in terms of its radius is s(r)=4pi(r^2), estimate the rate at which the volume

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-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?

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 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?

2. ### 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?

3. ### 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.

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

1. ### 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?

2. ### 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.

3. ### Calculus: need clarification to where the #'s go

Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 \mbox{cm}^3\mbox{/s}. How fast is the surface area of the balloon increasing when its radius is 14 \mbox{cm}? Recall that a ball of radius r

4. ### 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