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3-D Formula - Right Circular Cylinder

A cylinder is one of the most basic curvilinear geometric shapes. The surface formed by points at a fixed distance from a given straight line is the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder.

A cylinder has a round base and a given height. The area of the base must be found first, and then it can be multiplied by the height to give the volume of the cylinder. The area of the base is given by taking the radius (r) of the circular base and squaring it and then multiplying it by pi.

There are some variations on the theme as regards the shape of a cylinder. The classic shape is a right circular cylinder.  In common usage, a cylinder is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces. If the cylinder has a radius r and length (height) h, then its volume is given by:

V = \pi r^2 h \,

and its surface area is:
the area of the top ( \pi r^2 )\,+

the area of the bottom ( \pi r^2 )\,+

the area of the side ( 2 \pi r h )\,.

Therefore without the top or bottom lateral area, the surface area is A = 2 \pi r h.\,

With the top and bottom, the surface area is

A = 2 \pi r^2 + 2 \pi r h = 2 \pi r ( r + h ).\,

right circular cylinder

Solving for volume:

right circular cylinder volume

 
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