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Question
The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. 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 be h = 100 cm
Volume (original) of a solid right circular cylinder = πr2h
= π × (100)2 × 100
= 1000000π cm3
New radius = r' = 80 cm
New height = h' = 110 cm
∴ Volume (New) of a solid right circular cylinder = πr'2h'
= π × (80)2 × 110
= 704000π cm3
∴ Decrease in volume = Original volume – New volume
= 1000000π cm3 – 704000π cm3
= 296000π cm3
Percentage change in volume = `"Decrease in volume"/"Original volume" xx 100%`
= `(296000pi cm^3)/(1000000pi cm^3) xx 100%`
= 29.6%
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