Problem Solving

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such cannisters that could be used, what is the radius, in inches, of the one that has maximum volume?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Should be C - 5

Vol of cylinder = pi*r^2*h
8 and 10 are bigger nos so the cylinder will have max volume with diameter and height from these nos.

Now, you have to max out r^2*h and that would happen when diameter of cylinder is 10 and height is 8

So radius of cuylinder = 5

What's the OA?

I believe the answer should be 4.

The radius can never be 5 , since the cube always has one smaller side adjacent to the bigger side (10). And the max diameter would be the shorter side (8) .

OA please

ans is 4...
Raul..can u explain in detail....

wot i thot was...
volume of rectangular wooden box is 6*8*10 = 480

now volume of cylinder pi*r^2*h; taking h as max side = 10

so pi*r^2*h = 480
pi*r^2*10 = 480
r^2 = 48/pi
r approx is 3.1

so i selected 3
which is wrong...

Thanks raulverde. I got it

Consider each side at a time

1. Take 6x8 as a base and 10 as height. diameter cannot be more than 6.

vol of cylinder = pi*3^2*10 = 90pi

2. Take 8x10 as a base and 6 as height. radius = 4
vol = pi*4^2*6=96pi

3. Take 6x10 as a base and 8 as height. radius =3
Vol = pi*3^2*8=pi*72

radius for max volume = 4

I got stuck at this question too, but did not understand raul's point. Could someone please explain why radius can not be "5" ?

This is a OG 11 question and u can see the detailed ans there if u want. But to understand this picture a rectangular box with dimension 10*8*6, it can have rectangles with the following dimensions

10*8
10*6
8*6

If the radius of the cylinder is 5 its diameter is 10. Now picture keeping this cylinder with a diameter of 10 on a rectangular piece of paper with dimension of 10* 8. U will see the cylinder will come out from one side which measures 8 cms

For radius to be 5 u need at least one side to be 10* 10

Excellent ri2007. I understood it now! Thank you very much.