Example 11 from Algebra and Trigonometry, 1.1 Real Numbers: Algebra Essentials

Using a Formula

A right circular cylinder with radius $r$ and height $h$ has the surface area $S$ (in square units) given by the formula $S = 2 π r (r + h) .$ See Figure 3. Find the surface area of a cylinder with radius 6 in. and height 9 in. Leave the answer in terms of $π .$

A right circular cylinder with an arrow extending from the center of the top circle outward to the edge, labeled: r. Another arrow beside the image going from top to bottom, labeled: h.

Figure 3 Right circular cylinder

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Evaluate the expression $2 π r (r + h)$ for $r = 6$ and $h = 9.$

$\begin{matrix} S & = & 2 π r (r + h) \\ = & 2 π (6) [(6) + (9)] \\ = & 2 π (6) (15) \\ = & 180 π \end{matrix}$
The surface area is $180 π$ square inches.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

A photograph with length L and width W is placed in a mat of width 8 centimeters (cm). The area of the mat (in square centimeters, or cm²) is found to be $A = (L + 16) (W + 16) - L \cdot W .$ See Figure 4. Find the area of a mat for a photograph with length 32 cm and width 24 cm.

/ An art frame with a piece of artwork in the center. The frame has a width of 8 centimeters. The artwork itself has a length of 32 centimeters and a width of 24 centimeters.

Figure 4

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Figure 4

Solution

Your turn

Solution

Your turn