The volume of a cone is 9856 cu cm. If the diameter of its base is 28 cm, what is its height and its slant height?

We have

Given: diameter of the base of the cone = 28 cm

⇒ radius, r = 28/2 = 14 cm

Volume of the cone = 9856 cm³

We know,

Volume of cone = 1/3 πr²h

⇒

⇒

⇒

⇒

So, we have r = 14 cm and h = 48 cm. In right-angled ∆COB, using Pythagoras theorem

CB² = OB² + CO²

⇒ l² = r² + h², where l = slant height

⇒ l² = 14² + 48²

⇒ l² = 196 + 2304 = 2500

⇒ l = √2500 = 50

Thus, height is 48 cm and slant height is 50 cm.