Posted by Joshie on Wednesday, October 6, 2010 at 5:09pm.
gas is pumped into a spherical balloon at the rate of 1 cubic feet per minute. How fast is the diameter of the balloon increasing when the balloo0n contains 36 cubic feet of gas?
- calculus - Reiny, Wednesday, October 6, 2010 at 5:27pm
V = (4/3)πr^3
when V = 36 ...
36 = (4/3)πr^3
r^3 = 27/π
r = 2.04835
dV/dt = 4πr^2 dr/dt
1 = 4π(2.04835^2) dr/dt
dr/dt = .018966 ft^3/min
since diameter = 2r
d(diameter)/dt = .0379 ft^3 /min
- calculus - Damon, Wednesday, October 6, 2010 at 5:35pm
first find dr/dt. The diameter changes twice as fast as the radius.
v = (4/3) pi r^3
dv/dt = 4 pi r^2 dr/dt
1 = 4 pi (r^2) dr/dt
but r^3 = (3/4)(36)/pi
so r = 2.05 ft
1 = 4 pi (4.2) dr/dt
dr/dt = .019 ft/min
D = 2 r
dD/dt = 2 dr/dt = .038 ft/min
rate of volume increase = surface area * dr/dt
1 = 4 pi r^2 * dr/dt
same old equation
- calculus - Jorge, Thursday, November 8, 2012 at 5:37pm
A spherical balloon is inflated so that its volume is increasing at the rate of 2.2 ft^3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.2 feet?
Answer This Question
More Related Questions
- Calculus - Air is being pumped into a spherical balloon and the volume is ...
- calculus - Air is being pumped into a spherical balloon so that its volume ...
- Calculus - Air is being pumped into a spherical balloon so that its volume ...
- Calculus - a spherical balloon is inflated with gas at the rate of 500 cubic ...
- calculus - a spherical balloon filled with gas has a leak that permits the gas ...
- Calculus - A spherical balloon is inflated at the rate of 5 cubic feet/minute. ...
- Calculus - A spherical party balloon is being inflated with helium pumped in at ...
- Calculus - A spherical balloon is inflated at a rate of 10 cubic feet per minute...
- math-calculus - A spherical party balloon is being inflated with helium pumped ...
- calculus - A spherical balloon is being inflated at a rate of 10 cubic inches ...