What is a Cylinder?

Cylinder
The cylinder is formed by rotating any rectangle with a side on the axis of rotation

Volume Formula:
V=?r^2h

Surface Area Formula:
SA=2?r^2+2?rh

Relationship between the volume and surface area when a particular plane figure is rotated around two different axes of rotation such as the x-axis and y-axis:

When you rotate rectangle OBCD around the y-axis, you get a cylinder. The radius is 4 and the height is 3.

When you rotate rectangle OBCD around the x-axis you get a cylinder. The radius is 3 and the height is 4.

Cylinder around the y-axis: V = ?4^2(3) = 48? (cubic units)
SA=2?(4)^2+2?(4)(3) = 56? (square units)

Cylinder around the x-axis: V = ?3^2(4) = 36? (cubic units)
SA=2?(3)^2+2?(3)(4) = 42? (square units)

Ratio: Volume y:x = 4:3
Surface Area y:x = 4:3