Question

A man has to make arrangements for the accommodation of 150 people in a tent. He plans to build a tent which is the shape of a cylinder surmounted by a cone. Each person occupies 4 sq.m of the space on ground and 40cu.m of air to breathe. What should be the height of the cone if the height of the cylinder is 8m?

Answer 1

Answer:

The height of the cone is 6m.

Step-by-step explanation:

Since each person is required (occupies) 4m2 of space on the ground.

∴ ∴ Area of base = 150 x Required (area for one person)  = 150 x 4 m2  = 600 m2 ∴

∴  πr2 = 600 ----(1)

Now, the volume of the formed tent  

volume of required air inside the tent  = 150 x volume of required air to breadth each person

= 150 x 40 m3  = 600 m3 ∴

∴  πr2 (8 + h/3) = 6000 ⇒ 8 + h/3 =  6000

π r^2= 6000/600 = 10

6000πr^2=6000/600=10 ⇒ h/3 = 10 - 8 = 2 ⇒ h = 6 m

Hence, the height of the conical part of the tent is 6m.