Question

The curved surface area of a right circular cylinder is 308 cm². If the ratio of its total surface area and curved area is 2:1, then find its volume.

Answer 1

Given:

Curved (lateral) surface area (CSA) = 308 cm2.

Total surface area (TSA): CSA

= 2:1 ⇒ TSA

= 2 × 308

= 616 cm²

Let r be radius and h be height. Using standard cylinder formulae CSA = 2πrh and TSA = 2πr(h + r).

From CSA: 2π r h = 308.       ...(1)

TSA = CSA + 2π r²

= 616

⇒ 308 + 2π r²

= 616

⇒ 2π r² = 308.          ...(2)

From (2): r² = `308/(2π)`.

Take π = `22/7`: r²

= `(308 × 7)/(2 × 22)`

= 49 

r = 7 cm.

From (1): 2 × `22/7` × 7 × h = 308

⇒ 44 h = 308

⇒ h = 7 cm.

Volume V = π r² h

= `22/7` × 7² × 7

= 1078 cm³.