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Question
The ratio between the radius of the base and the height of a cylinder is 2 : 3. find the total surface area of the cylinder, it its volume is 1617 cm3.
Solution
Data given is as follows:
`r/h = 2/3`
Volume = 1617 cm3
We have to find the Total surface area
From the given data, we have
`r/h = 2/3`
Therefore, `h = 3/2r`
Also, we know that
Volume = `pir^2h`=1617
`pir^2h` =1617
`xx 22/7 xx r xx r3/2 xx r` =1617
`r^3 = 343`
r =7 cm
`h = 3/2 xx7`
`h = 21/2` cm
Therefore, total surface area is
`TSA = 2 pir( r +h)`
`⇒ TSA = 2 xx 22/7 xx 7 (7 +21/2)`
`⇒ TSA = 770 cm^2`
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