## Basic Shape Stuff

### Geometry Help

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The perimeter is the outside line that makes up the shape. In a circle, the length of the perimeter is called the circumference.

The radius is the distance from the center of a circle to the perimeter. The diameter is 2 times the radius.

### 3-D objects

#### Volume

The volume of a box is length x width x
height.

**Example:** A box that is 3 m long by 2 m wide by 4 m high has a
volume of 3 x 2 x 4 = 24 cubic m.

The volume of a cylinder is
(Pi)r^{2}h where r is the radius of the cylinder and h is the
height.

**Example:** A cylinder with a radius of 4 and height of 6 has a
volume of Pi x 16 x 6 = 301.5929 rounding to 4 decimals.

The volume of a pyramid with a square base
of length L and height h is L^{2}h/3.

**Example:** A pyramid with a square base of length 4 and height of 9
has a volume of 16(9)/3 = 48.

The volume of a cone is
(Pi)r^{2}h/3. Essentially it uses the formula for the volume of
a cylinder and divides it by 3.

**Example:** If a cone has a radius of 4 and height of 6, its volume
is 75.3982/3 = 25.1327.

The volume of a sphere is (4/3)(Pi)r^{3}.

**Example:** A sphere with a radius of 4 has a volume of
(4/3)(Pi)(64) = 268.0826.

#### Surface area

To get the surface area of a box, cube or pyramid, compute the area of each side and add them up.

The surface area of a cylinder is
2(Pi)rh where r is the radius of the cylinder and h is the
height.

**Example:** A cylinder with a radius of 4 and height of 6 has a
surface area of 2 x Pi x 4 x 6 = 150.7964 rounding to 4 decimals.

The surface area of a sphere is
4(Pi)r^{2}.

**Example:** A sphere with a radius of 4 has a surface area of
4(Pi)(16) = 201.0619.

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