Question

A conical vessel has a slant height of 25 cm, and its Curved surface area 175π cm². Find the volume of the conical vessel.

1. 1232
2. 1322
3. 1223
4. 1242

Answer 1

Correct Answer - Option 1 : 1232

Given:

Slant height = 25 cm

Curved surface area = 175π cm²

Formula used:

C.S.A = πrl

Volume of cone = 1/3 πr²h

Where r = radius, h = height, l = slant height, C.S.A = Curved Surface Area

Calculation:

175π = πr × 25

⇒ r = 175π/25π = 7 cm

Using triplet (7, 24, 25)

⇒ h = 24 cm

Volume of cone = (1/3) × (22/7) × (7)² × 24

⇒ Volume = 1232 cm³

∴ The volume of conical vessel is 1232 cm³