Question

A solid cylinder has TSA of 462cm.square .Its CSA is one third of its TSA .Find the volume of the cylinder.

Answer 1

Answer : 538 cm³

Step-by-step explanation :

Total Surface Area of cylinder

= 2πr( h + r ) or 2πrh + 2πr²

Curved Surface Area = ⅓ Total Surface Area

2πrh = ⅓ × 462 cm²

2πrh = 154 cm²

Since 2πrh + 2πr² = 462 cm²

154 cm² + 2πr² = 462 cm²

2πr² = 462 - 154 cm²

2πr² = 308 cm²

r² = 308/2π

r² = 308 × 1/2 × 7/22 cm²

r² = 28 × 1/2 × 7/2 cm²

r = √49 cm² = 7 cm

Therefore, 2πrh = 154 cm²

h = 154/2 × 1/(πr)

h = 154 × 1/2 × 7/22 × 1/7 cm

h = 3.5 cm

Volume of cylinder = πr²h

Volume of cylinder = 22/7 × 7² × 3.5 cm³

Volume of cylinder = 539 cm³