jimjohn wrote:

A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

Answer: The radius of the cylinder must be equal to half of the smaller of the 2 dimensions that form the box's bottom. ............... and teh answer is 200 x pi

I just don't understand why does the radius half to be equal to half of the smaller of the 2 dimensions. does anyone understand why? thx.

Its helpful to draw this out.

1st Cyl. L,W,H : 12,10,8

Greatest diameter we can have is 10. (can't be 12 b/c it wouldnt fit in the box). So radius is equal to 5.

pir^2h = Vol of Cyl.

pi5^2*8 25*8=200.

2nd Cyl: L,W,H: 10,8,12

pi4^2*12 --> 16*12 =192

3rd Cyl: L,W,H: 8,10,12

No need to calculate as we can see this is going to be smaller than 2.

Dimensions L,W,H: 12,10,8 result in the greatest volume for a cylinder.

In answer to ur question. Draw a square, forget the cube.

Do dimensions 12 and 10. Now draw a line from the midpoint of one side of the square to another side of the square.

now draw a circle. you will see that only when the diameter is 10 will it actually fit in the box.