Question

The ratio of the radius and height of a cylinder is 2:3. If its volume is 12,936 cm³, find the total surface area of the cylinder.

Answer 1

The ratio of the radius and height of a cylinder = 2:3

Let the radius of the cylinder be 2x and the height of the cylinder be 3x.

Volume of the cylinder = 12936 cm³

∵ Volume of a cylinder = πr²h

∴  `12936 = 22/7 xx (2x)^3 xx 3x`

⇒ `12936 = 22/7 xx 4x^2 xx 3x`

⇒ `12936 = 264/7 x^3`

⇒ `x^3 = (12936 xx 7)/264 = 49 xx 7`

⇒ x³ = 7 × 7 × 7 = (7)³

⇒ x³ = (7)³

∴ x = 7

So, radius 2x = 2 × 7 = 14 cm and height = 3x = 3 × 7 = 21 cm

The total surface area of the cylinder = 2πr(r + h)

= `2 xx 22/7 xx 14(14 + 21)`

= `(44 xx 14)/7 xx 35`

= 44 × 14 × 5

= 3080 cm²