Question

A solid cylinder has a total surface area of 231cm3. Its curved surface area is 2 3 of the total surface area. Find the volume of the cylinder

Answer 1

Step-by-step explanation:

The surface area of solid cylinder = 231 cm²

and curved surface area = 2/3 * 231 cm² = 154 cm²

Now, 2πrh = 154 ...........(i)

2πrh+2πr² = 231

Subtracting, 2πr² = 231 - 154 = 77

⇒2 * 22/7 * r² = 77

⇒r² = 77*7/2*22 ⇒ 49/4 ⇒ (7/2)²

so, r = 7/2 cm

Now, from (i),

2 * 22/7 * 7*h/2 = 154

⇒22h = 154 ⇒ 154/22 = 7

and volume = πr²h = 22/7 * 7/2 * 7/2 * 7cm³ ⇒ 539/2 = 269.5 cm²