Question

The total surface area of a solid right circular cylinder is 231cm². Its curved surface area is two thirds of the total surface area.Find the radius and height of the cylinder.

Answer 1

Answer:

Total surface area of a solid circular cylinder = 231 cm²

Its curved surface area = 2πrh

Total surface area = 2πrh + 2πr²

2πrh + 2πr² = 231............. - (1)

Curved surface area is 2/3rd of the total surface area

Therefore,

2πrh = 2/3 * 231

2πrh = 154................ - (2)

Substituting value of 2πrh from equation (2) into equation (1), we get,

154 + 2πr² = 231

2πr² = 231 - 154

2πr² = 77

2 * 22/7 * r² = 77

44/7 r² = 77

r² = 77 / 44/7

r² = 77 * 7 / 44

r² = 539 / 44

r² = 12.25

r = √12.25

r = 3.5 cm

Substituting r's value in equation (2), we get,

2 * 22/7 * 3.5 * h = 154

(44 * 3.5)h / 7= 154

22h = 154

h = 154 / 22

h = 7 cm

Therefore, radius = 3.5 cm and height = 7 cm.