Volume And Surface Area Of Solids | Volume And Surface Area Of Solids Exercise 15C

Question

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5m.

Find the volume of the cone.

Accepted Answer

ANSWER:

We know that

Curved surface area of the tent = area of the cloth = 165 m2

So we get

Πrl = 165

By substituting the values

(22/7) × 5 × l = 165

On further calculation

l = (165 × 7)/ (22 × 5) = 21/2 m

We know that

h = √ (l2 - r2)

By substituting the values

h = √ ((21/2)2 - 52)

On further calculation

h = √ ((441/4) – 25) = √ (341/4)

So we get

h = 9.23m

We know that

Volume of the tent = 1/3 πr2h

By substituting the values

Volume of the tent = 1/3 × (22/7) × 52 × 9.23

On further calculation

Volume of the tent = 241.7 m3

Question 21