Please solve:Ques :130 OG

[swati.sug]

The inside dimensions of a rectangular box are 6 inches by 8 inches by 10 inches.A cylindrical canister is to be placed inside the box so that is stands upright when the closed box rests on one of its six faces.Of all such canisters that could be used what is the radius in inches ,of one that has maximum volume?
A 3
B 4
C 5
D 6
E 8

[swati.sug]

Sorry Question No is 191 from OG 11

[pandeyvineet24]

hi Swati,

The Cylinder with the maximum volume will be the one with a radius 5. Basically the trick is that one side of the rectangle will be the diameter of the cylinder.

Volume = (pi)r^2H

Volume will be highest when r = 5 and the height =8 which is 200(Pi)
hence answer is C.

Volume of other cylinders are 150(pi), 90(pi), 160(pi), 72(pi), 96(pi)

[swati.sug]

Hii..
OA is b) 4 in OG.
Coming to your explaination.You consider that radius will be 5 and dia 10.
But if i have a rectangle and I need to inscribe a circle in it the maximum diameter can be the length of the smaller side,right?

So if in this problem we take base as 10*8 the maximum dia can be 4.
In this case volume will be Pi* 4^2 * 6 =96 *pi

Now if we take base as 6 by 8 and height 10
Vol = pi *3^2 * 10 = 90pi


Therfore answer is 4.
Hey I got the answer while trying to explain it to you
Thanks

[andes1]

is 8