The ratio between the curved surface area and the total surface area o

1.	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» 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.

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»

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.