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.

Answer 1

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