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

Question

A solid cylinder has a total surface area of 231 cm². It curved surface area is \(\frac{2}{3}\) of the total surface area. Find the volume of the cylinder.

Answer 1

Given,

Total surface area of cylinder = 231 cm²

Curved surface area = \(\frac{2}{3}\) total surface area = \(\frac{2}{3}\) x 231 = 154 cm²

so,

= 2πrh = \(\frac{2}{3}\) 2πr(r + h)

= 3 h = 2h + 2r

= h = 2r.............(i)

And,

= 2πr(r + h) = 231

= 2 x \(\frac{22}{7}\) x r x 3r = 231(putting h = 2r)

= r² = \(\frac{231\times 3\times 7}{44}\) = \(\frac{49}{4}\)

= r = \({\sqrt\frac{49}{4}}\) = \(\frac{7}{2}\) = 3.5 cm

= h = 2r = 2×3.5 = 7 cm

Volume of cylinder = πr²h = \(\frac{22}{7}\) x 3.5 x 3.5 x 7 = 269.5 cm³