Question

A store sells two fish tanks.
• The small fish tank is 12 inches long, 8 inches wide, and 6 inches high.
• The large fish tank is 8 inches wide and 6 inches high.
• The volume of the large fish tank is two times the volume of the small fish tank.
Part A
What is the volume of the small fish tank? Enter the answer in the box.
cubic inches
Part B
How long is the large fish tank? Enter the answer in the box.

Answer 1

To find the answers to the two parts, we can start with Part A.

### Part A: Volume of the Small Fish Tank

The formula for the volume \( V \) of a rectangular prism (which is the shape of the fish tanks) is given by:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

For the small fish tank:
- Length = 12 inches
- Width = 8 inches
- Height = 6 inches

Now, we calculate the volume:

\[
V = 12 \, \text{inches} \times 8 \, \text{inches} \times 6 \, \text{inches}
\]

Now perform the multiplication step-by-step:

1. \( 12 \times 8 = 96 \)
2. \( 96 \times 6 = 576 \)

So, the volume of the small fish tank is

\[
\boxed{576} \, \text{cubic inches}
\]

### Part B: Length of the Large Fish Tank

We know the volume of the large fish tank is two times the volume of the small fish tank:

\[
V_{\text{large}} = 2 \times V_{\text{small}} = 2 \times 576 \, \text{cubic inches} = 1152 \, \text{cubic inches}
\]

The dimensions of the large fish tank are given as:
- Width = 8 inches
- Height = 6 inches
- Let Length = \( L \) inches (unknown)

Using the volume formula for the large fish tank:

\[
V = L \times \text{width} \times \text{height}
\]
\[
1152 \, \text{cubic inches} = L \times 8 \, \text{inches} \times 6 \, \text{inches}
\]

We can simplify this:

\[
1152 = L \times 48
\]

Now, we will isolate \( L \):

\[
L = \frac{1152}{48}
\]

Calculating the division:

\[
L = 24 \, \text{inches}
\]

Thus, the length of the large fish tank is

\[
\boxed{24} \, \text{inches}
\]