# 11.2: Surface Area of Prisms and Cylinders

Difficulty Level: At Grade Created by: CK-12

## Learning Objectives

• Find the surface area of a prism.
• Find the surface area of a cylinder.

## Review Queue

1. Find the area of a rectangle with sides:
1. 6 and 9
2. 11 and 4
3. 52\begin{align*}5\sqrt{2}\end{align*} and 86\begin{align*}8\sqrt{6}\end{align*}
2. If the area of a square is 36 units2\begin{align*}36 \ units^2\end{align*}, what are the lengths of the sides?
3. If the area of a square is 45 units2\begin{align*}45 \ units^2\end{align*}, what are the lengths of the sides?
4. Find the area of the shape. All sides are perpendicular. (Split the shape up into rectangles.)

## Review Questions

1. How many square feet are in a square yard?
2. How many square centimeters are in a square meter?

Use the right triangular prism to answer questions 3-6.

1. What shape are the bases of this prism? What are their areas?
2. What are the dimensions of each of the lateral faces? What are their areas?
3. Find the lateral surface area of the prism.
4. Find the total surface area of the prism.
5. Writing Describe the difference between lateral surface area and total surface area.
6. The lateral surface area of a cylinder is what shape? What is the area of this shape?
7. Fuzzy dice are cubes with 4 inch sides.
1. What is the surface area of one die?
2. Typically, the dice are sold in pairs. What is the surface area of two dice?
8. A right cylinder has a 7 cm radius and a height of 18 cm. Find the surface area.

Find the surface area of the following solids. Leave answers in terms of \begin{align*}\pi\end{align*}.

1. bases are isosceles trapezoids

Algebra Connection Find the value of \begin{align*}x\end{align*}, given the surface area.

1. \begin{align*}SA = 432 \ units^2\end{align*}
2. \begin{align*}SA = 1536 \pi \ units^2\end{align*}
3. \begin{align*}SA = 1568 \ units^2\end{align*}
4. The area of the base of a cylinder is \begin{align*}25 \pi \ in^2\end{align*} and the height is 6 in. Find the lateral surface area.
5. The circumference of the base of a cylinder is \begin{align*}80 \pi \ cm\end{align*} and the height is 36 cm. Find the total surface area.
6. The lateral surface area of a cylinder is \begin{align*}30 \pi \ m^2\end{align*}. What is one possibility for height of the cylinder?

Use the diagram below for questions 23-27. The barn is shaped like a pentagonal prism with dimensions shown in feet.

1. What is the area of the roof? (Both sides)
2. What is the floor area of the barn?
3. What is the area of the sides of the barn?
4. The farmer wants to paint the sides of the roof (excluding the roof). If a gallon of paint covers 250 square feet, how many gallons will he need?
5. A gallon of paint costs \$15.50. How much will it cost for him to paint the sides of the barn?
6. Charlie started a business canning artichokes. His cans are 5 in tall and have diameter 4 in. If the label must cover the entire lateral surface of the can and the ends must overlap by at least one inch, what are the dimensions and area of the label?
7. An open top box is made by cutting out 2 in by 2 in squares from the corners of a large square piece of cardboard. Using the picture as a guide, find an expression for the surface area of the box. If the surface area is \begin{align*}609 \ in^2\end{align*}, find the length of \begin{align*}x\end{align*}. Remember, there is no top.
8. Find an expression for the surface area of a cylinder in which the ratio of the height to the diameter is 2:1. If \begin{align*}x\end{align*} is the diameter, use your expression to find \begin{align*}x\end{align*} if the surface area is \begin{align*}160\pi\end{align*}.

1. 54
2. 44
3. \begin{align*}80 \sqrt{3}\end{align*}
1. \begin{align*}s = 6\end{align*}
2. \begin{align*}s = 3 \sqrt{5}\end{align*}
3. \begin{align*}A = 60 + 30 + 20 = 110 \ cm^2\end{align*}

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