Mensuration prob #3

[papgust]

A conical tent is to accomodate 10 persons. Each person must have 6 metre square space to sit and 30 metre cube of air to breathe. What will be the height of the cone?

I don't have the OA for this one. Can someone put forward the correct steps leading to the solution?

[vivekjaiswal]

A conical tent is to accomodate 10 persons. Each person must have 6 metre square space to sit and 30 metre cube of air to breathe. What will be the height of the cone?

I don't have the OA for this one. Can someone put forward the correct steps leading to the solution?

Given that each person should have a 6 m.sq. of area, that means the base should have a total area of 6*10 = 60 m.sq. (which is pi*r^2, r being the radius of the base)

The volume of the cone will have to be 30*10 m.cube. as each person needs 30 m.cube volume. Thus using the expression for the volume of a cone
1/3 pi*r^2*h = 300
Now pi*r^2 = 60, thus the above expression becomes
(1/3)*60*h=300 => h=15 m.

Cheers,
Vivek

[papgust]

Thanks vivek for the solution!