The radius of the base and the height of a cylinder are in the ratio 2:3. If its volume is find the total surface area of the cylinder.

Question

Philoid · Accepted Answer

Given,

Volume of cylinder = 1617 cm³

Ratio of radius of base and height = 2 : 3

Let base radius = 2x cm

Let height = 3x cm

Volume = πr²h

=

= x³ =

= x³ = 42.875

= x =

Hence,

Radius of cylinder = 2 × 3.5 = 7 cm

Height of cylinder = 3 × 3.5 = 10.5 cm

Total surface area of cylinder = 2πrh + 2πr² = 2πr (h + r) = 2 × × 7 × 17.5 = 770 cm²