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by jainrahul1985 » Wed Jan 05, 2011 10:14 pm
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?

OA 200pi

Please let me know any short cut to slove this question .

Source : Manhattangmat
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by Rahul@gurome » Wed Jan 05, 2011 10:28 pm
Solution:
Volume of cylinder is pi*r^2*h.
For maximum volume, radius should be maximum because it has a square power.
This is possible if we take the base of cylinder as the base of the box which is 12*10.
Then the diameter is 10 for the cylinder, as it has to be lesser of 10 and 12.
Or radius is 10/2 = 5 and height is 8.
So volume is pi * 5^2 * 8 = 200pi.
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by shovan85 » Wed Jan 05, 2011 10:28 pm
jainrahul1985 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?

OA 200pi

Please let me know any short cut to slove this question .

Source : Manhattangmat
Volume of a Cylinder = pie* radius^2 * height

In the concerned rectangular boxes the
1) base can be 12 * 10 and height 8
or 2) base can be 10*8 and height 12
or 3) base can be 8*12 and height 10

In each case of base the Radius will be the half of the length of width (lesser length)

Case 1. r = 5 h =8 then V = pie(5)^2 (8) = 200pie
Case 2. r = 4 h =12 then V = pie(4)^2 (12) = 182pie
Case 3. r = 4 h =10 then V = pie(4)^2 (10) = 160pie

Answer is 200pie
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