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?
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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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