# 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.

1. 332 cm²
2.  269.5 cm²
3.  314.2 cm²
4.  32 cm²

Anurag Mishra Professor Asked on 26th January 2016 in

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.

Anurag Mishra Professor Answered on 26th January 2016.