Question

find the rate of change of a cylinder whnen its radius is 6 feet if its height is always 3/2 times its radius and its increasing a the rate of 2 feet per minute

Answer 1

324π ft³/ min  the rate of change of a cylinder.

What is the volume of the cylinder?

• The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it.
• Cylinder's volume is given by the formula, πr2h, where r is the radius of the circular base and h is the height of the cylinder.
• Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.

Find  dV/dt

h = 3r/2

Volume of cylinder V = πr²h

  v = πr²(3r/2)

   v = 3/2 πr³

   differentiate both side

$\frac{dv}{dt} = 3 . \frac{3}{2} \pi r^{2} dr/dt$

$\frac{dv}{dt} = 3 . \frac{3}{2} \pi 6^{2} (2)$  = 324π ft³/ min

Learn more about volume of a cylinder

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