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Question
The total surface area of a solid cylinder is 616 cm2. If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.
Solution
Let r and h be the radius and height of a solid cylinder.
Total surface area of a cylinder = 616 cm2
`=>` 2πr(h + r) = 616
`=> pir(h + r) = 616/2`
`=>` πr(h + r) = 308 ...(i)
Curved surface area of a cylinder = 2πrh
Now, `"Curved surface area of a cylinder"/"Total surface area of a cylinder" = 1/2`
`=> (2pirh)/(2pir(h + r)) = 1/2`
`=> h/(h + r) = 1/2`
`=>` 2h = h + r
`=>` 2h – h = r
`=>` h = r
Substituting h = r in (i), we get
`=>` πr(r + r) = 308
`=>` πr.2r = 308
`=>` 2πr2 = 308
`=>` πr2 = 154
`=> 22/7 xx r^2 = 154`
`=> r^2 = (154 xx 7)/22`
`=>` r2 = 49
`=> r = sqrt(49)`
`=>` r = 7 cm
`=>` h = 7 cm.
∴ Volume of cylinder = πr2h
= `22/7 xx 7 xx 7 xx 7`
= 1078 cm3
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