Question

The radius of a solid Right Circular Cylinder increases by 20% and its height decreases by 20% find percentage change in volume?

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Answer 1

Given original

• radius = r
• height = h

Given new

• radius = r' = r + (20/100)r = r + r/5 = 6r/5
• height = h' = h - (20/100)h = h - h/5 = 4h/5

Thus original volume;

V = πr²h

Thus new volume;

V' = πr'²h'

• π(6r/5)²(4h/5)
• π×(36r²/25)(4h/5)
• π × 144r²h/125

Thus change in volume;

• ∆V = V' - V
• πr²h ( 144/125 - 1)
• πr²h (144 - 125)/125
• πr²h ( 19/125)

Thus % increase ;

• ∆V/V × 100
• { (19/125)πr²h / πr²h } × 100
• 19/125 × 100
• 19/5 × 4
• 76/5 = 15.2%

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