Wednesday

April 16, 2014

April 16, 2014

Posted by **Becky** on Saturday, August 11, 2012 at 4:19pm.

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 5:07pmgiven 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 12:04amHi 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 12:19pmi get the answer already! thank you!

**Related Questions**

Geometry - The wheel of an adult's bicycle has diameter 26 in. The wheel of a ...

physics - Omar races his bicycle for 152m. A wheel of his bicycle turns 38times ...

algebra - Justin races his bicycle for 90M . A wheel of his bicycle turns 45 ...

Math - Juan races his bicycle for 196ft a wheel of his bicycle turns 28 times as...

Math - A wheel on Greg's bicycle is 0.3 m in diameter. Greg races the bicycle ...

math - The diameter of a bicycle wheel is 65cm. How far does the bicycle go in ...

Math - A bicycle wheel is 30 inches in diameter. a. To the nearest revolution,...

math - This is an SAT prep question. Senai customized her bicycle by exchanging...

math - If a bicycle wheel has a diameter of 63 centimeter. During A journey the ...

Precalc - 1. If a bicycle wheel has a diameter of 27 inches, find the radian ...