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Question
The ratio between the radius of the base and height of a cylinder is 2 : 3. If its volume is 1617 cm3, find the total surface area of the cylinder.
Solution
Given data is as follows
`r/h =2/3`
volume of the cylinder = 1617 cm3
We have to find the total surface area of this cylinder
It is given that `r/h = 2/3`
Therefore ` h = 3/2 r`
volume of the cylinder = `pi r^2h`
Therefore;
`pir^2h = 1617`
`22/7 r^2 xx 3/2 xx r = 1617 (" As h" = 3/2r)`
r = 7
So;
`h=3/2xx7`
`=21/2`
Therefore;
Total surface area = `2pirh + 2 pir^2`
=`2pi r(h + r)`
=`2xx22/7xx7(21/2)+7`
= 770 cm2
T.S.A = 770 cm2
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