Find the volume of a cone-shaped figure if its base has a radius of 7 cm and its slant height is 25 cm.

We have

Given: radius of cone, r = 7 cm

Slant height of cone, l = 25 cm

We need to find volume of the cone.

First, let’s find height of this cone.

In right-angled ∆BOC, using Pythagoras theorem,

BC² = BO² + OC²

⇒ OC² = BC² – BO²

⇒ OC² = 25² – 7²

⇒ OC² = 625 – 49 = 576

⇒ OC = √576 = 24

⇒ height of cone, h = 24 cm

Now, volume of cone is given by

Volume = 1/3 πr²h

Substituting r = 7 cm and h = 24 cm in above equation,

⇒

⇒

Thus, volume is 1232 cm³.