Find the volume of a cone, if its total surface area is 7128 sq.cm and radius of base is 28 cm.
(π = 22/7)

Question

Find the volume of a cone, if its total surface area is 7128 sq.cm and radius of base is 28 cm.(π = 22/7)

Philoid · Accepted Answer

Given: Total surface area of cone (TSA) = 7128 cm²

Radius of base of cone (r) = 28 cm

We know total surface area of cone is given by,

TSA = πrl + πr²

⇒ πrl = TSA – πr²

⇒

⇒ l = 53

So, slant height of cone = 53 cm

We have,

Using Pythagoras theorem in ∆AOB, we can find height of the cone.

AB² = AO² + OB²

⇒ AO² = AB² – OB²

⇒ h² = 53² – 28²

⇒ h² = 2809 – 784

⇒ h = √2025 = 45

We have got height (h) = 45 cm.

Volume of cone is given by,

V = πr²h/3

⇒

⇒ V = 36960

Thus, volume of cone is 36960 cm³.