To find out how much glass is needed to enclose the aquarium, we need to calculate the surface area of the rectangular prism (box) defined by its dimensions.
The formula for the surface area \( S \) of a rectangular prism is:
\[ S = 2(lw + lh + wh) \]
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
Now we can calculate each of the products:
- \( lw = 17 \times 9 = 153 \)
- \( lh = 17 \times 11 = 187 \)
- \( wh = 9 \times 11 = 99 \)
Now, we can substitute these values back into the surface area formula:
\[ S = 2(153 + 187 + 99) \]
Calculating the sum inside the parentheses:
\[ 153 + 187 + 99 = 439 \]
Now multiplying by 2:
\[ S = 2 \times 439 = 878 \]
Thus, the total surface area of the aquarium, which is the amount of glass needed, is:
\[ \text{Surface area} = 878 \text{ square inches} \]
So the answer is:
surface area = 878 square inches