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?
Accepted Solution
A:
Given dimensions:Height of the cylinder = 2 mVolume is increasing at a rate of = 10 m³/minRadius = 4 inchesConverting radius in meters.1 inch = 0.0254 meters4 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.