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.

Answer 1

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