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, if its volume is 1617 cm³.

Answer 1

We have,

Ratio between radius and height of a cylinder = 2:3

r/h = 2/3

h = 3/2 r

Volume of cylinder = 1617 cm³

πr²h = 1617

22/7 × r² × 3/2r = 1617

r³ = 1617×7×2 / 22×3

= 343

r = ³√343

= 7cm

Radius = 7 cm

Height = 3/2r = 3/2 × 7 = 21/2 = 10.5cm

∴ Total surface area of cylinder = 2πr (h+r)

= 2 × 22/7 × 7 (10.5+7)

= 770 cm²