To calculate the amount of glass needed to enclose the aquarium, we need to find the surface area of the rectangular prism (the aquarium). The surface area \( S \) of a rectangular prism can be calculated using the formula:
\[ S = 2lw + 2lh + 2wh \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given the dimensions:
- Length \( l = 17 \) inches,
- Width \( w = 9 \) inches,
- Height \( h = 11 \) inches.
Let's substitute these values into the formula:
-
Calculate \( 2lw \): \[ 2lw = 2 \times 17 \times 9 = 306 \]
-
Calculate \( 2lh \): \[ 2lh = 2 \times 17 \times 11 = 374 \]
-
Calculate \( 2wh \): \[ 2wh = 2 \times 9 \times 11 = 198 \]
Now, sum these results to find the total surface area:
\[ S = 306 + 374 + 198 = 878 \text{ square inches} \]
Thus, Tommy and Cole need to buy 878 square inches of glass to enclose the aquarium.