To find the amount of glass needed to enclose the aquarium, we need to calculate the surface area of the rectangular prism (box) formed by the aquarium. The formula for the surface area \( S \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is given by:
\[ S = 2(lw + lh + wh) \]
Given the dimensions of the aquarium:
- Length \( l = 17 \) inches
- Width \( w = 9 \) inches
- Height \( h = 11 \) inches
Now, we can plug these values into the surface area formula:
\[ S = 2( (17)(9) + (17)(11) + (9)(11) ) \]
Calculating each term inside the parentheses:
- \( 17 \times 9 = 153 \)
- \( 17 \times 11 = 187 \)
- \( 9 \times 11 = 99 \)
Now, add these results together:
\[ 153 + 187 + 99 = 439 \]
Now multiply by 2 to get the total surface area:
\[ S = 2 \times 439 = 878 \]
Thus, the total surface area of the aquarium, and the amount of glass they need to buy, is:
\[ \text{surface area} = 878 \text{ square inches} \]