Question: --------------------------------------------------------------------------------

1. Show that a volume of a cylinder equals to v = A² / (4πh)
where h= height of the cylinder
A = area of a original paper

how would i prove this question?
could any one please help
thank you

v = π r² h -------1
v = A² / (4πh) -----2

If you rolled a sheet of paper of length x and width h to form a cylinder then the height of the cylinder is h and the circumference of the end of the cylinder is x.

If r is the radius of the circle at the end of the cylinder then the circumference is 2 π r. But the circumference is x so

x = 2 π r

The area of the sheet of paper A is x times h and hence

A = 2 π r h

Solve this equation for r and substitute the value for r into the expression you know for the volume of a cylinder v = π r² h.

Penny