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 $\pi = \frac{22}{7}$)
Answer & explanation
Correct answer: option 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