Question

A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r, decreases. If the length of the cylinder is increasing by 0.8 cm per second, find the rate at which the radius is changing when the radius is 2 cm and the length is 11 cm. (Give units.)

Answer 1

Answer:

$0.0727 cm\: per\: second$

Step-by-step explanation:

The Volume of the cylinder is constant

Volume of a cylinder, $V=\pi r^2h$

Given:

$\frac{dh}{dt}=0.8 cm/sec\\ r=2cm\\h=11cm\\\frac{dr}{dt}=?$

$\frac{dV}{dt}=\pi r^2 \frac{dh}{dt} + 2\pi r h\frac{dr}{dt}$

$0=\pi* 2^2*0.8 + 2\pi*2*11\frac{dr}{dt}\\0=3.2\pi+44\pi\frac{dr}{dt}\\44\pi\frac{dr}{dt}=-3.2\pi\\\frac{dr}{dt}=\frac{-3.2\pi}{44\pi} \\\frac{dr}{dt}=-0.0727 cm\: per\: second$

The radius is decreasing at a rate of $0.0727 cm\: per\: second$