Question

There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m, of the ground inside the tent. If height of the tent is 18 m, find the volume of the tent.

Answer 1

Given: For the tent, height (h) = 18 m, number of people in the tent = 25, area required for each person = 4 sq.m 

To find: Volume of the tent 

i. Every person needs an area of 4 sq.m, of the ground inside the tent. 

Surface area of the base of the tent = number of people in the tent × area required for each person 

= 25 × 4 

= 100 sq.m

ii. Surface area of the base of the tent = πr² 

∴ 100 = πr² 

∴ πr² = 100

iii. Volume of the tent = (1/3) πr²h 

= (1/3) x 100 x 18 ...[∵ πr² = 100] 

= 100 x 6 

= 600 cubic metre 

∴ The volume of the tent is 600 cubic metre.