Posted by Becky on Saturday, August 11, 2012 at 4:19pm.
A bicycle wheel has a diameter D = 60 cm and the tyre has a cross sectional radius of r = 2.5 cm. The volume V of the inner tube is given by
V = pi^2 D r^2 + (8/3*pi*r^3)
If air is being pumped into the tyre so that the volume of the inner tube is increasing at the rate of 12 cm3/sec, what is the rate at which the cross sectional radius r of the inner tube is increasing in cm/sec? (Assume the diameter D is not changing.)
Correct a decimal number to 3 significant figures.

calculus  Steve, Saturday, August 11, 2012 at 5:07pm
given V as above,
dV/dt = (2pi^2 D r + 8pi r^2) dr/dt
now plug in the numbers, assuming that at the time of interest, r = 2.5cm :
12 = (2pi^2*60*2.5 + 8pi*2.5^2) dr/dt
dr/dt = 6/(25pi(6pi+1))= 0.0038 cm/s

calculus  Becky, Sunday, August 12, 2012 at 12:04am
Hi thanks for helping. But when differentiate pi^2 isn't that is 2pi? How come your answer is 2pi^2? and when different r^2 isn't that is 2r? How come your equation is dv/dt = 2pi^2 D r + 8/3*pi*r^2? Because my answer is 2pi D 2r + 8/3*pi*r*^2. anyone can explain? Thanks!

calculus  Becky, Sunday, August 12, 2012 at 12:19pm
i get the answer already! thank you!
Answer This Question
Related Questions
 Geometry  The wheel of an adult's bicycle has diameter 26 in. The wheel of a ...
 Math  An inner tube for a bicycle has a diameter of 2 inches and measures ...
 Math  An inner tube for a bicycle has a diameter of 2 inches and measures ...
 math  an inner tube for a bicycle has a diameter of 2 inches and measures about...
 Physics, URGENT!!!  We consider tobacco virus diffusing along a 0.47 m long ...
 Physics  A bicycle wheel has a diameter of 47.6 cm and a mass of 0.809 kg. The ...
 physics  A bicycle wheel has a diameter of 57.7 cm and a mass of 2.66 kg. The ...
 Physics  A bicycle wheel has a diameter of 47.6 cm and a mass of 0.809 kg. The ...
 maths help  Hi MY question is if a cylinder has a volume of 72cm cubed and a ...
 physics  A bicycle wheel has a diameter of 64.2 cm and a mass of 1.79 kg. ...
More Related Questions