Question

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the volume of the cylinder, if its total surface area is 616 cm².

Answer 1

Total surface area (T.S.A) = 616 cm²

Let r be the radius of cylinder and h be the radius of cylinder. 

As per given statement: 

(curved surface area / (total surface area) = \(\frac{1}{2}\) 

or CSA =  \(\frac{1}{2}\)TSA 

CSA =  \(\frac{1}{2}\) x 616 = 308 

⇒ CSA = 308 cm² 

Now, 

TSA = 2πrh + 2πr² 

⇒ 616 = CSA + 2πr² 

⇒ 616 = 308 + 2πr² 

⇒ 2πr² = 616 – 308 

⇒ 2πr² = 308

⇒ r² = 308/2π

⇒ r² = 49 

or r = 7 cm …(1) 

As, CSA = 308 cm² 

2πrh = 308 

⇒ 2 x \(\frac{22}{7}\) x 7 x h = 308 (using (1)) 

⇒ h = 7 cm 

Now, 

Volume of cylinder = πr²h 

= \(\frac{22}{7}\) x 7 x 7 x 7 

= 1078 

Therefore, Volume of cylinder is 1078 cm².