a rectangular piece in cylinder

Question

a rectangular piece of cardboard measuring 12 by 16 is folded into a cylinder akong one of its sides, what's the maximal volume of the cylinder:

1. 576/pi

2. 768/pi

3. 861/pi

4. 192pi

5.784pi

i do not have the OA.

jamifahad · Answer

V=pi r^2 h
Max volume when r is max.
hence r=8 (folded such that side 16 forms diameter)
V=pi 8^2 * 12
=768pi

OA B.

dimri10 · Answer

that's tha answer i got, but the answers declare: 766 divided by pi

subhashghosh · Answer

There are two ways of doig this :

1 in which circumference = 2*pi*r = 12 => r = 6/pi and height = 16 => volume = pi * 36/pi^2 * 16 = 576/pi

2 in which circumference = 2*pi*r = 16 => r = 8/pi and height = 12 => volume = pi * 64/pi^2 * 12 = 768/pi

Answer - B

dimri10 · Answer

the first step is important:

concluding that 12 or 16 are the circumference was based on what premise? 
the Q was saying that the measure of the box were 12/16 or am i missing somthing?

subhashghosh · Answer

It's like this :
When you roll a piece of paper into a cylinder, the length or breadth becomes a circle of the base. Now the perimeter of this circle is equal to the length of the side, and the perimeter of a circle = circumference of a circle. You can try to roll a paper and you'll get the idea.

dimri10 · Answer

THANK'S. i imagined it quite differently. you treated that like a roll and i treated it as sitting on tha radius. that's great

subhashghosh · Answer

Yup, as I said, trying to do this in real life can give valuable insight into how the 3-D figures look like. Glad to help

puneetj · Answer

v= pi*r^2*h
use r=6, h = 16 and calculate
use r= 8 and h = 12 and calculate

B...

a rectangular piece in cylinder

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