Surface Area: Prisms, Cylinders, Pyramids, Cones, Spheres

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]

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

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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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