Question

A solid cylinder has a total surface area of 42 sq.cm. Its curved
surface area is one third of its total surface area. Find the volume of
the cylinder.

Answer 1

We have Total Surface Area of cylinder

= 2πr( h + r ) or 2πrh + 2πr²

2πrh + 2πr² = 462 cm² _(i)

Where,

Curved Surface Area = ⅓ Total Surface Area

2πrh = ⅓ × 462 cm²

2πrh = 154 cm²

Substituting value of 2πrh in eq (i),

154 cm² + 2πr² = 462 cm²

2πr² = 462 - 154 cm² = 308 cm²

r² = 308/2π

r² = 308 × 1/2 × 7/22 cm²

r² = 28 × 1/2 × 7/2 cm²

r = √49 cm² = 7 cm

Substituting value of r in 2πrh

2πrh = 154 cm²

h = 154/2πr

h = 154 × 1/2 × 7/22 × 1/7 cm

h = 7/2 cm

Volume of cylinder = πr²h

= 22/7 × 7² × 7/2 cm³

= 539 cm³

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