Smriti Shashikumar wrote:Find the maximum volume of the cylinder that can fit in a cuboid with dimensions 6 , 8, and 10 respectively.
A. 90pi
B. 96pi
C. 150pi
D. 200pi
E. 384pi
Volume of cylinder = pi(radius^2)(height)
There are 3 different ways to position the cylinder (with the base on a different side each time).
You can place the base on the 6x8 side, on the 6x10 side, or on the 8x10 side
If you place the base on the 6x8 side, then the cylinder will have height 10, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6).
So, the volume of this cylinder will be (pi)(3^2)(10), which equals
90(pi)
If you place the base on the 6X10 side, then the cylinder will have height 8, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6).
So, the volume of this cylinder will be (pi)(3^2)(8), which equals
72(pi)
If you place the base on the 8x10 side, then the cylinder will have height 6, and the maximum radius of the cylinder will be 4 (i.e., diameter of 8).
So, the volume of this cylinder will be (pi)(4^2)(6), which equals
96(pi)
So, the greatest possible volume is [spoiler]96(pi) = B[/spoiler]
Cheers,
Brent
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