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Question
The height and the radius of the base of a cylinder are in the ratio 3 : 1. If it volume is 1029 π cm3; find it total surface area.
Solution
Ratio between height and radius of a cylinder = 3 : 1
Volume = 1029 πcm3 ...(1)
Let radius of the base = r
Then height = 3r
∴ Volume = πr2h
= π × r2 × 3r
= 3πr3 ...(2)
From (1) and (2)
3πr3 = 1029π
`r^3 = 1029/3pi = 343`
r = 7
Therefore, radius = 7 cm and height = 3 × 7 = 21 cm
Now, total surface area = 2πr(h + r)
= `2 xx 22/7 xx 7 xx (21 + 7)`
= `2 xx 22/7 xx 7 xx 28`
= 1232 cm2
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