The ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm³, then find its total surface area (take π = 3.14).

3391.2 cm²

We know that,

Volume of cylinder = πr²h

TSA of cylinder = 2πr(r + h)

Height : radius = 7 ∶ 5.

Volume = 14836.5 cm³ 

Let the height be 7a and radius be 5a

Now,

Volume = π (5a)² × 7x

= 14836.5 = (3.14)(25a²) × 7a

= 14836.5 = (3.14)(25a²) × 7a

= 175a³ = \(\frac{14836.5}{3.14 }\)

= a³ = \(\frac{4725}{175}\)

= a = 3

Now,  Radius = 5a =  5 × 3 = 15 cm

Height = 7a = 7 × 3 = 21 cm

For TSA of cylinder,

TSA = 2(3.14) × 15 × (15 + 21) = 6.28 × 15 × 36 = 3391.2 cm²