Question

in a right circular cylinder of height 2 meters, if the volume is increasing at 10 m^3/min how fast is the radius of the cylinder increasing when the radius is 4in?

Answer 1

Given dimensions:

Height of the cylinder = 2 m

Volume is increasing at a rate of = 10 m³/min

Radius = 4 inches

Converting radius in meters.

1 inch = 0.0254 meters

4 inches = $4\times0.0254=0.1016$ meters

$\frac{dv}{dt}=10$

we have to find, $\frac{dr}{dt}=?$

Volume of the cylinder is given by $\pi r^{2} h$

= $\pi r^{2} *2 = 2\pi r^{2}$

Now differentiating with respect to 't'

$\frac{dv}{dt} = \frac{d}{dt} (2\pi r^{2})$

$\frac{dv}{dt} = 2\pi (2r)(\frac{dr}{dt})$

$10=2\pi (2*0.1016)\frac{dr}{dt}$

$10=2*3.14(0.2032)\frac{dr}{dt}$

$\frac{dr}{dt}=\frac{10}{1.276}$

= 7.83 meter per minute.