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Biggest Cylinder in a Box

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by mchaubey » Thu May 06, 2010 12:55 pm
A large rectangular box is 4 feet wide, 5 feet long, and 8 feet tall. A metal cylinder is to be fitted snugly into the box and stood upright on its base, resting on any one of the 6 sides of the box. Of all such cylinders that could fit into the box, what is the diameter, in feet, of the one that has the largest possible volume?

a. 2
b. 2.5
c. 4
d. 5
e. 8
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by clock60 » Thu May 06, 2010 1:08 pm
mchaubey wrote:A large rectangular box is 4 feet wide, 5 feet long, and 8 feet tall. A metal cylinder is to be fitted snugly into the box and stood upright on its base, resting on any one of the 6 sides of the box. Of all such cylinders that could fit into the box, what is the diameter, in feet, of the one that has the largest possible volume?

a. 2
b. 2.5
c. 4
d. 5
e. 8
base of the box 4*5 with d=4 and h=8, volume=pi*4*8=32*pi

base of the box 5*8 with d=5 and h=4, volume=pi*2,5^2*4=25*pi

base of the box 8*4 with d=4 and h=5, volume=pi*4*5=20*pi

so i got C with diameter=4
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by mchaubey » Thu May 06, 2010 6:22 pm
C is correct but Why couldn't it be 5

The total volume of cylinder with diameter 5 and height 8 would be 157
and volume of the box will be 5*4*8= 160
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by neerajkumar1_1 » Thu May 06, 2010 6:31 pm
mchaubey wrote:C is correct but Why couldn't it be 5

The total volume of cylinder with diameter 5 and height 8 would be 157
and volume of the box will be 5*4*8= 160
it cant be as your base is 4 X 5 , so u cant fit a cylinder of diameter 5 when one side of the box is of side 4.
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by debmalya_dutta » Thu May 06, 2010 7:25 pm
Base of the box is a rectangle of 5 by 4 dimension and the cylinder base should fit that dimension . remember that the diameter of the cylinder should fit the base both lengthwise (5) and width wise (4) .
So the diameter of the cylinder is 4

the diameter cannot be 5 because you cannot fit a circle of diameter = 5 in a rectangle of dimensions 5 by 4
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