To find the volume of the fish tank, you can use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given dimensions:
- Length = \( 36 \frac{1}{2} \) in = \( 36.5 \) in
- Width = \( 12 \frac{3}{4} \) in = \( 12.75 \) in
- Height = \( 18 \frac{1}{2} \) in = \( 18.5 \) in
Let's calculate the volume:
\[ \text{Volume} = 36.5 \times 12.75 \times 18.5 \]
Calculating step-by-step:
- First calculate \( 36.5 \times 12.75 \):
\[ 36.5 \times 12.75 = 465.875 \]
- Next, multiply that result by \( 18.5 \):
\[ 465.875 \times 18.5 = 8618.1875 \]
Now, let's convert this to a mixed fraction format:
The decimal \( 8618.1875 \) can be separated into whole and fractional parts:
- Whole part: \( 8618 \)
- Fractional part: \( 0.1875 \)
Now convert \( 0.1875 \) to a fraction:
\[ 0.1875 = \frac{1875}{10000} = \frac{3}{16} \]
(After simplifying)
Thus, the volume of the tank is:
\[ 8618 \frac{3}{16} \text{ in}^3 \]
Since none of the offered choices exactly matches, it's good to note they could be in slightly different formats or approximations. Checking the closest one:
- \( 8609 \frac{7}{16} \text{ in}^3 \) is the only volume among the options that is reasonably close to \( 8618.1875 \).
However, the accurate calculated volume is approximately:
\[ 8618.1875 \text{ in}^3 \text{ or } 8618 \frac{3}{16} \text{ in}^3 \]
While it doesn't exactly match the options, if only one choice were to be selected:
The volume of the tank is closest to 8,609 7/16 in^3.