Chapter 12 Toolbox

What is a lateral face?

A lateral face is any side of an object that is not a base.

What is a base?

A base is the “bottom” and “top” of a shape/prism. A shape will have a maximum of two bases.

What is lateral area?

Lateral area is the total area of the sides of a 3D shape, EXCLUDING the bases.

How do we find the lateral area of a prism?

L = Ph

To find the lateral area of a prism, we find the perimeter (P) of its base and multiply times its height.

What is “surface area”?

Surface area is the sum of the area of a shape’s lateral area AND the area of its bases.

For example, if you would to paint the surface area of a water bottle, you would only paint the outside of the water bottle.

How do we find the surface area of a prism?

S = Ph + 2B / S = L + 2B

To find the surface area of a prism, calculate the lateral area and add the areas of the two bases. In other words:

Surface area = Perimeter of base(height) + 2(area of base) OR Surface area = lateral area + 2(area of base)

How do we find the surface area of a cylinder?

S = 2πrh + 2(πr²) / S = L + 2B

To find the surface area of a cylinder, calculate the lateral area (circumference of the base * height), then add the areas of the two circular bases. In other words:

Surface area = 2πrh + 2(πr²)

Surface area = lateral area + 2(area of base)

What is a “slant height”?

A slant is is the height of each lateral face of a period.

How do we find the lateral area of the pyramid?

L = ½ Pl

Lateral area of a pyramid = 1/2 * perimeter of the base * slant height

*Note that in your book, slant height is represented by a cursive lowercase “l.”

How do we find the surface area of a pyramid?

S = ½ P l + B / S = L + B

To find the surface area of the pyramid, add the lateral area and the area of the base. In other words:

Surface area of a pyramid = (½ *the perimeter of the base * slant height) + the area of the base.

How do we find the lateral area of a cone?

L = πrl

To find the lateral area of a cone, we multiply pi by the radius by the slant height. In other words:

lateral area of a cone = pi*radius*slant height

How do we find the surface area of a cone?

S = πrl + πr²

To find the surface area of a cone, find the lateral of a cone and add the area of the base (πr²).

What is “volume”?

Volume is the amount of 3D space filled by an object. In other words, if you were to fill an object with water, how much water would you need?

How do you find a volume of a prism?

V = Bh

To find the volume of a prism, multiply the area of the base of the prism by its height.

How do we find the volume of a cylinder?

V = πr²h / V = Bh

To find the volume of a cylinder, multiply the area of its base (πr²) by its height.

How do we find the volume of a pyramid?

V = 1/3(Bh)

To find the volume of a pyramid, multiple the area of the base and the height by a 1/3.

How do we find the volume of a cone?

V = 1/3(πr²h)

To find the volume of a cone, multiply the area of the base times its height and multiply it by a 1/3.