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