Question

The radius of the base and the height of a cylinder are each increased by 10%, then by wna
percent does the volume of the cylinder increase?​

Answer 1

The Percentage increase in the volume of the cylinder is  72 .8%

Step-by-step explanation:

Let the radius of the cylinder be r and height be h.

volume of cylinder "V" = πr^2h

New radius = r+20 / 100 r = 65 r

New height = h+20 / 100 h = 65 h

Therefore, New Volume V1 = π(65)^2×(65 h)

                                             = 216 / 125 πr^2 h

Increase in volume = 216 / 125 πr^2h − πr^2h

                                 = 91 / 125 πr^2 h

Percentage increase = 91 / 125πr^2h ÷ πr^2 h×100 = 72 .8%

Thus the Percentage increase in the volume of the cylinder is  72 .8%

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