Question

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

Answer 1

We have,

Total surface area of cylinder = 231 cm²

Curved surface area = 2/3 total surface area = 2/3 × 231 = 154 cm²

2πrh = 2/3 2πr(h + r)

3h = 2(h+r)

3h = 2h + 2r

h = 2r ……… (i)

And,

2πr(h + r) = 231

2 × 22/7 × r × (2r+r) =231

2 × 22/7 × r × 3r = 231

3r² = 231×7 / 2×22

= 1617 / 44

= 36.75

r² = 36.75 / 3

= 12.25

r = √12.25

= 3.5 cm

Since, h = 2r = 2×3.5 = 7cm

∴ Volume of cylinder = πr²h

= 22/7 × 3.5 × 3.5 × 7

= 269.5 cm³