The ratio of radius of the base and the height of solid right circular cylinder is 2 : 3. If its volume is 202. 125 cm$^3$, then its total surface area is: (Take $\pi = \frac{22}{7}$)

192.5 $cm^2$

We know that,

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

Voulme of cylinder = πr²h

We have,

Volume = 202.125 cm³

Radius : Height = 2n : 3n

According to the question,

πr²h = 202.125

= \(\frac{22}{7}\) × 2n × 2n × 3n = 202.125

= n³ = \(\frac{202.125 × 7}{(12 × 22 }\)

= n = \(\frac{3.5}{2}\)

= n = 1.75

So, the radius of cylinder = 2 × 1.75 = 3.5

Height of cylinder = 3 × 1.75 = 5.25

= Total surface area of cylinder = 2 × \(\frac{22}{7}\) × 3.5 (3.5 + 5.25) = 192.5