Question

a solid cylinder has tsa 924 cm2 and csa is 2/3 of tsa. find radius, height and volume of cylinder

Answer 1

Given total surface area = 924 cm²
⇒ 2πrh + 2πr² = 924 cm²
⇒ 2πrh = 924 - 2πr² → A
Curved surface area = 2/3*924 = 616 cm²
⇒ 2πrh = 616 cm² → B
From A and B
924 - 2πr² = 616
2πr² = 924-616 = 308
r² = 308*7/(22*2) = 49 cm [taking π = 22/7]
r =  7 cm

2πrh = 616
h = 616*1/2*7/22*1/7 = 14 cm
Height of cylinder = 14cm and radius = 7 cm

Volume of cylinder = πr²h = 22/7*7*7*14 = 2156 cm³