Shipment

[umaa]

A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?





4



5



6



8



10

[sjd00d]

Is it 6? To maximize the volume (pi*r^2*h), we need to maximize first r and then h, take radius of 12 and height of 10.

[Alara533]

IMO radius should be 5

The cylinder can stand on any of the six faces, creating 3 cases

1) 10 * 8 base and 12 height
In this case Volume would be (Pi)r2H = 4 * 4 * 12 * (pi)
Since on 10*8 base, the cylinder can have a max radius of 4

2) 10 * 12 base and 8 height
Volume = 5 * 5 * 8 * (pi)

3) 12 * 8 base and 10 height
Volume = 4 * 4 * 10 * (pi)

Out of this 2nd case gives max volume i.e. 200(pi), for radius 5.

[ontopofit]

IMO 5

if it is 6 it wont fit in:D

[umaa]

OA is 5.

[DeepakR]

Can someone explain how the radius was chosen in each of the 3 cases Alara mentioned ?

Thanks

[semidevil]

You need to picture the tank inside the box. suppose the tank was inside a box, then the outer rim of the tank will be the radius and diameter. The radius and diameter falls along the z axis of the box.