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 = [tex]4\times0.0254=0.1016[/tex] meters
[tex]\frac{dv}{dt}=10[/tex]
we have to find, [tex]\frac{dr}{dt}=?[/tex]
Volume of the cylinder is given by [tex]\pi r^{2} h[/tex]
= [tex]\pi r^{2} *2 = 2\pi r^{2}[/tex]
Now differentiating with respect to 't'
[tex]\frac{dv}{dt} = \frac{d}{dt} (2\pi r^{2})[/tex]
[tex]\frac{dv}{dt} = 2\pi (2r)(\frac{dr}{dt})[/tex]
[tex]10=2\pi (2*0.1016)\frac{dr}{dt}[/tex]
[tex]10=2*3.14(0.2032)\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{10}{1.276}[/tex]
= 7.83 meter per minute.
