Question
George built a fish tank. How many cubic inches of water are needed to completely fill the fish tank?
Do you need to find the surface area or volume of the prism in order to solve this problem?
Right triangular prism. Base of the triangular base measures 10 in and its height measures 18 in. The height of the prism measures 12 in.
George's fish tank
Surface Area
Volume
Nice!
This fish tank is in the shape of a prism. To find its volume, you need to multiply the area of the base by the height. Start by finding the area of the base on paper, then record your answer on Zearn. You can use the calculator if you need to.
Right triangular prism. Base of the triangular base measures 10 in and its height measures 18 in. The height of the prism measures 12 in.
George's fish tank
Area of
the base, B Height of
the prism, h Volume
V = B ยท h
in2
Do you need to find the surface area or volume of the prism in order to solve this problem?
Right triangular prism. Base of the triangular base measures 10 in and its height measures 18 in. The height of the prism measures 12 in.
George's fish tank
Surface Area
Volume
Nice!
This fish tank is in the shape of a prism. To find its volume, you need to multiply the area of the base by the height. Start by finding the area of the base on paper, then record your answer on Zearn. You can use the calculator if you need to.
Right triangular prism. Base of the triangular base measures 10 in and its height measures 18 in. The height of the prism measures 12 in.
George's fish tank
Area of
the base, B Height of
the prism, h Volume
V = B ยท h
in2
Answers
GPT-4o mini
To find out how many cubic inches of water are needed to completely fill the fish tank, you need to calculate the volume of the right triangular prism that represents the tank.
### Step 1: Find the area of the triangular base (B)
The triangular base has a base (b) of 10 inches and a height (h) of 18 inches. The area of a triangle is given by the formula:
\[
B = \frac{1}{2} \times \text{base} \times \text{height}
\]
Plugging in the values:
\[
B = \frac{1}{2} \times 10 \, \text{in} \times 18 \, \text{in}
\]
\[
B = \frac{1}{2} \times 180 \, \text{in}^2 = 90 \, \text{in}^2
\]
### Step 2: Calculate the volume of the prism (V)
Now that we have the area of the base, we can calculate the volume of the prism. The volume formula for a prism is:
\[
V = B \times h
\]
Where \( B \) is the area of the base and \( h \) is the height of the prism. In this case, the height of the prism is given as 12 inches.
\[
V = 90 \, \text{in}^2 \times 12 \, \text{in}
\]
\[
V = 1080 \, \text{in}^3
\]
### Conclusion
The volume of the fish tank is **1080 cubic inches**. This is the amount of water needed to completely fill the tank.
### Step 1: Find the area of the triangular base (B)
The triangular base has a base (b) of 10 inches and a height (h) of 18 inches. The area of a triangle is given by the formula:
\[
B = \frac{1}{2} \times \text{base} \times \text{height}
\]
Plugging in the values:
\[
B = \frac{1}{2} \times 10 \, \text{in} \times 18 \, \text{in}
\]
\[
B = \frac{1}{2} \times 180 \, \text{in}^2 = 90 \, \text{in}^2
\]
### Step 2: Calculate the volume of the prism (V)
Now that we have the area of the base, we can calculate the volume of the prism. The volume formula for a prism is:
\[
V = B \times h
\]
Where \( B \) is the area of the base and \( h \) is the height of the prism. In this case, the height of the prism is given as 12 inches.
\[
V = 90 \, \text{in}^2 \times 12 \, \text{in}
\]
\[
V = 1080 \, \text{in}^3
\]
### Conclusion
The volume of the fish tank is **1080 cubic inches**. This is the amount of water needed to completely fill the tank.