3-D Objects

Volume of cube = s³ where s is the length of any edge of the cube.

Surface area of cube = 6s²Where s is the length of any edge of the cube.

The volume enclosed by a pyramid is one third of the base area times the perpendicular height. As a formula:

Where b is the area of the base of the pyramid and h is its height. The height must be measured as the vertical distance from the apex down to the base.

The total surface area of any pyramid, is sum of the surface areas of each face. In the case of a right pyramid, the side faces are all the same, so we can simply find the area of one and multiply by the number of faces. Once we add the area of the base, we have the total surface area.

How to find the volume of a cylinder?

Although a cylinder is technically not a prism, it shares many of the properties of a prism. Like prisms, the volume is found by multiplying the area of one end of the cylinder (base) by its height.

Since the end (base) of a cylinder is a circle, the area of that circle is given by the formula:

Multiplying by the height h we get

where:
π is Pi, approximately 3.142
r is the radius of the circular end of the cylinder
h height of the cylinder

The surface area of a cylinder can be found by breaking it down into three parts:

The two circles that make up the ends of the cylinder.
The side of the cylinder, which when "unrolled" is a rectangle

Aprism has two congruent, parallel faces called the bases of the prism. The volume of any prism can be found by multiplying the area of one of the bases by its height. In the case of a triangular prism, each base is a triangle.

As a formula where a is the area of one triangular end face, and h is the height.

A right prism is composed of a set of flat surfaces.

The two base are congruent polygons.
The lateral faces (or sides) are rectangles.

The total surface area of a right prism is the sum of these.