A carpet of dimensions 30 meters by 40 meters by 1 cm is rolled into a cylinder with length 30 meters and diameter "D". What is "D", assuming the carpet experiences no change in volume when it is ideally rolled into a perfect cylinder with no hole in the center?

Question

valpey · Answer

The cross section of the cylinder should have area 40m x 1cm = 0.4 m^2 and will be a circle.
The area of a circle is pi*r^2 and D is 2*r so:
$$0.4m = \pi *r^2$$
$$\sqrt{0.4m/\pi} = r$$
$$ 2*\sqrt{0.4m/\pi} =D$$

anonymous · Answer

how did you get that the area was 40 m by 1 cm?

valpey · Answer

The carpet is 30m x 40m x 1cm (volume) and the cylinder is 30m long so while the volume of the cylinder is equal to 30m x 40m x 1cm, when we divide out the length of the cylinder we get the area of the cross section.

valpey · Answer

You can think of it also as the cross-sectional area of the carpet before it is rolled as 40m x 1cm.

anonymous · Answer

What do you mean by the cross section? Could you possibly draw it for me? I'm still a little confused.

valpey · Answer

The carpet is like a very wide and long but short box. We can always look at the cross-sectional area of a box by ignoring one of its dimensions. In this case we ignore the 30m dimension.

valpey · Answer

Can you imagine the cross-sectional area of the cylinder as a spiral of carpet? If you unroll the cross-sectional spiral, how long will it be?