**Definition: **The surface area is the sum of all the areas of all the shapes that cover the surface of the object.

Prism:

Surface Area = 2*(area of base) + perimeter*height

[SA = 2A + ph]

Cylinder:

Surface Area = 2*(area of base) + 2*pi*radius*height

[SA = 2πr² + 2πrh]

Pyramid:

Surface Area = (area of base) + 1/2(slant*perimeter)

[SA = A + 1/2pl]

l = slant height

Cone:

Surface Area = (area of base) + 1/2*circumference*slant

[SA = πr² + πrl] or [SA = πr(r + l)]

Sphere:

Surface Area = 4 * pi * radius * radius

[SA = 4πr²]

**Example: **Find the surface area of the figure to nearest tenth:

**Solution: **

Determine the appropriate surface area formula for this figure and plug in the given values.

Step 1: Identify the figure.

As this figure has two parallel, congruent, circular bases, we know it is a cylinder and can apply the following formula:

Surface Area = 2*(area of base) + 2*pi*radius*height

Step 2: Plug the given values into the formula.

This figure has a height of 14 in, and a base radius of 7 in. Plugging this information into the formula we get:

Surface Area = 2(7²π) + 2π*7*14

Step 3: Simplify to find the surface area.

SA = 2(7²π) + 2π*7*14

SA = 2(49π) + 196π

SA = 98π + 196π

SA = 294π = 923.6

Because surface area is always measured in square units, we will label this answer as:

SA = 923.6 square in or 923.6 in²

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