# What is the volume of the cylinder made of a 8*12 sheet rolled longside?

hala718 | Certified Educator

We have a rectangular sheet with length = 12 and width = 8.

The rectangle is rolled long-side to shape a cylinder.

Then the height of the cylinder will be the length of the rectangle= 12.

==> The height (h) = 12.

Then, the width of the rectangle will form the circumference of the base.

==> The circumference C = 8.

Now we will calculate the volume.

We know that the volume v = r^2 * pi * h where r is the radius of the base.

But we have C = 8

==> C = 2* pi * r = 8

==> r= 8/ 2*pi = 4/pi = 1.27 ( approx.)

Now we will substitute into the volume.

==> V = r^2 * pi * h

==> V = ( 4/pi)^2 * pi * 12

= 16/ pi * 12 = 61.12.

Then, the volume of the cylinder is 61.12 cubic units.

neela | Student

If you fold the sheet 8*12 along the longer side  and join the 2 paralle widths,  it becomes a cylinder of circumfernce 12 and height 8.

So the radius r of the cyliber whose circumference is 12 is given by :

r = circumference /2pi = 12/2pi = 6/pi.

The volume V of the cylinder whose radius is r  is given by:

V =( pi*r^2)h, where h = is height. Here,  r = 6/pi and h = 8

Therefore V = 2pi* (6/pi)^2 *8 = 576/pi = 183.35 cubic units.

Therefore the volume of the cylinder = 183.35 cubic units.