Question

The height and the radius of the base of a cylinder are in the ratio 3 : 1. If it volume is 1029 π cm³; find it total surface area.

Answer 1

Ratio between height and radius of a cylinder = 3 : 1 

Volume = 1029 πcm³  ...(1)

Let radius of the base = r 

Then height = 3r 

∴ Volume = πr²h

= π × r² × 3r

= 3πr³  ...(2)

From (1) and (2) 

3πr³ = 1029π

`r^3 = 1029/3pi = 343`

r = 7

Therefore, radius = 7 cm and height = 3 × 7 = 21 cm

Now, total surface area = 2πr(h + r)

= `2 xx 22/7 xx 7 xx (21 + 7)`

= `2 xx 22/7 xx 7 xx 28`

= 1232 cm²