Question

Nicholas has a fish tank that is 12 inches high, 14.5 inches long, and 6.5 inches wide. If he fills the tank halfway with water, how many cubic inches of water are in the tank?
141.375 cubic inches
282.75 cubic inches
565.5 cubic inches
1,131.0 cubic inches

Answer 1

To find the volume of water in the fish tank when it is filled halfway, we first need to calculate the total volume of the tank and then take half of that volume.

The formula for the volume of a rectangular prism (which is the shape of the tank) is:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

Given the dimensions of the tank:
- Height = 12 inches
- Length = 14.5 inches
- Width = 6.5 inches

Now, substituting in the values:

\[
\text{Volume} = 14.5 \, \text{inches} \times 6.5 \, \text{inches} \times 12 \, \text{inches}
\]

Calculating that step-by-step:

1. First, calculate the area of the base:
\[
\text{Base Area} = 14.5 \times 6.5 = 94.25 \, \text{square inches}
\]

2. Now multiply the base area by the height:
\[
\text{Volume} = 94.25 \times 12 = 1131.0 \, \text{cubic inches}
\]

Now, since Nicholas fills the tank halfway with water, we divide the total volume by 2:

\[
\text{Volume of water} = \frac{1131.0}{2} = 565.5 \, \text{cubic inches}
\]

Thus, the amount of water in the tank when filled halfway is **565.5 cubic inches**.