To calculate the surface area of the aquarium, which is in the shape of a rectangular prism, you can use the formula for the surface area \( S \) of a rectangular prism:
\[ S = 2lw + 2lh + 2wh \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length (\( l \)) = 17 inches,
- Width (\( w \)) = 9 inches,
- Height (\( h \)) = 11 inches.
Now, substitute the dimensions into the formula:
\[ S = 2(17)(9) + 2(17)(11) + 2(9)(11) \]
Calculating each term:
- \( 2(17)(9) = 306 \)
- \( 2(17)(11) = 374 \)
- \( 2(9)(11) = 198 \)
Now, add these results together:
\[ S = 306 + 374 + 198 = 878 \]
Thus, the total surface area of the aquarium is:
\[ \text{Surface area} = 878 \text{ square inches} \]
Therefore, Tommy and Cole need to buy 878 square inches of glass to enclose the aquarium.