Question

Dylan built an aquarium. How many cubic inches of water can fit in the aquarium?
Solve on paper, then enter your answer on Zearn. You can use the calculator to help you solve.
Triangular prism with side lengths labeled: 18 in, 10 in and 15 in
Dylan's aquarium
cubic inches of water can fit in the aquarium.

Answer 1

To calculate the volume of a triangular prism, you can use the formula:

\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]

First, we need to find the area of the triangular base. The formula for the area of a triangle given its side lengths (a, b, c) can be determined using Heron's formula:

1. Calculate the semi-perimeter \( s \):
\[
s = \frac{a + b + c}{2}
\]

2. Then, calculate the area \( A \):
\[
A = \sqrt{s(s-a)(s-b)(s-c)}
\]

Given the sides of the triangle: \( a = 18 \), \( b = 10 \), \( c = 15 \).

**Step 1:** Find the semi-perimeter \( s \):
\[
s = \frac{18 + 10 + 15}{2} = \frac{43}{2} = 21.5
\]

**Step 2:** Use Heron's formula to find the area \( A \):
\[
A = \sqrt{21.5(21.5 - 18)(21.5 - 10)(21.5 - 15)}
\]
Calculating each term:
- \( s - a = 21.5 - 18 = 3.5 \)
- \( s - b = 21.5 - 10 = 11.5 \)
- \( s - c = 21.5 - 15 = 6.5 \)

Now substitute these values back into the area formula:
\[
A = \sqrt{21.5 \times 3.5 \times 11.5 \times 6.5}
\]
Calculating the product:
- \( 21.5 \times 3.5 = 75.25 \)
- \( 11.5 \times 6.5 = 74.75 \)
- \( 75.25 \times 74.75 \approx 5625.0625 \)

Now take the square root:
\[
A \approx \sqrt{5625.0625} \approx 75
\]

**Step 3:** Now, using the area \( A = 75 \) square inches and the height of the prism (which we assume is the other dimension provided, 10 inches):
\[
\text{Volume} = A \times \text{Height} = 75 \times 10 = 750 \text{ cubic inches}
\]

Thus, the volume of the aquarium is:

\[
\boxed{750} \text{ cubic inches}
\]