Geometry - Circles & Cylinders Problem Set

[jayshree.pillai]

Hello Everyone,

I am having some trouble with Q#10, in Chap 3 of the Geometry Guide.

"A Rectangular box has dimensions 12X10X8. What is the largest possible volume of a right cylinder places inside the box"

I dont quite get the first line of solution that states:
"The radius of the cylinder = 1/2(smaller of the 2 dimensions that for box's bottom, the height can then be equal to remaining dimension of the box"

3 combinations have been considered, for this solution:

BaseXWidthX Height = Volume
8X12X10 = pi*(8/2)^2*10 =160pi
10X12X8 = pi*(10/2)^2*8 =200pi <-- Highest Volume
8X10X12 = pi*(8/2)^2*12 =192pi

My question is, why arent we considering this possiblity?
Base=10 & height = 12.
Since the cylinder rests on the base, radius would be = 10/2 = 5
In which case, the Volume would be = pi*5^2*12 = 300pi

Any advice would be highly appreaciated.

Thank you,
Jayshree

[jayshree.pillai]

Dear Instructors,

Any insight on this problem would be really helpful.

Thank you,
Jayshree

[shazmohdkhan]

Hi jayshree,

One must take into account that the largest radius of the cylinder that can fit in, will be half of the smaller dimension of the base.

So it would be 4 and not 5.

[esledge]

If the height is 12, the round base of the cylinder would sit on the 8-by-10 base of the box, so shazmohdkhan is absolutely right that a cylinder with radius 5 would be too big to fit.

The only reason you didn't catch this yourself is that you didn't draw a picture (am I right?). There's the take-away: draw a picture even when it seems unnecessary at first.