# A solid cylinder has a total surface area of 231 cm² Its curved surface area is 2/3 of the total surface area. Find.the volume of the cylinder.

- 332 cm²
- 269.5 cm²
- 314.2 cm²
- 32 cm²

**Answer: (2) 269.5 cm^3**

**Explanation:-**

Total surface area of a cylinder = 231 cm^2

Then, 2 pai x r(r + h) – 231 ………………. (1)

Curved surface area = 2/3 of total surface area (Given in the question)

Then, 2 x pai x r x h = 2 x 231/3

2 x pai x r x h = 154

h = 154/2 x pai x r …………………. (2)

From equation (1) ,

2 x pai x (r + 154/2 x pai x r) = 231

2 x pai x r^2 + 154 = 231

2 pai r^2 = 231 – 154

2 pai r ^2 = 77

r^2 = 77/2 pai

r^2 = 77 x 7 x 2/2 x 22 x 7

r^2 = 49/4

Square root on both side,

r = 7/2

From equation (2),

h = 154 x 7 x 2/2 x 22 x 7

h = 7 cm

Thus, volume of the cylinder = pai x r^2 x h

= 22 x 7 x 7 x 7 /7 x 2 x 2

= 11 x 7 x 7/2

= 539/2

= 269.5

Then, the volume of the cylinder is (2) 269.5 cm^3

Hence, the correct answer is option (2) 269.5 cm^3.