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Question
The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.
Solution
Let the radius of a solid right circular cylinder be r = 100 cm
And let the height of a solid right circular cylinder be h = 100 cm
∴ Volume (original) of a solid right circular cylinder
= πr2h
= π × (100)2 × 100
= 1000000π cm3
New radius = r' = 120 cm
New height = h' = 80 cm
∴ Volume (New) of a solid right circular cylinder = πr'2h'
= π × (120)2 × 80
= 1152000π cm3
∴ Increase in volume = New volume – Original volume
= 1152000π cm3 – 1000000π cm3
= 152000π cm3
Thus, Percentage change in volume = `"Increase in volume"/"Original volume" xx 100%`
= `(152000pi cm^3)/(1000000pi cm^3) xx 100%`
= 15.2%
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