Question
What is the volume of this prism?
Start by finding the area of the base of the prism. Solve on paper, and then enter your answer on Zearn. You can use the Zearn calculator to help with your calculations.
3D shape with pentagonal base composed of a rectangle with side lengths 4 cm by 6 cm, and a triangle atop the 6 cm length of the rectangle. The triangle is labeled with height 4 cm, and a side length of 3 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B · h
cm
2
? cm ? cm
3
Great job!
You just found that the area of the base is 36 cm
2
. Find the height of the prism, and then determine the volume.
3D shape with pentagonal base composed of a rectangle with side lengths 4 cm by 6 cm, and a triangle atop the 6 cm length of the rectangle. The triangle is labeled with height 4 cm, and a side length of 3 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B · h
36 cm
2
cm
cm
3
Start by finding the area of the base of the prism. Solve on paper, and then enter your answer on Zearn. You can use the Zearn calculator to help with your calculations.
3D shape with pentagonal base composed of a rectangle with side lengths 4 cm by 6 cm, and a triangle atop the 6 cm length of the rectangle. The triangle is labeled with height 4 cm, and a side length of 3 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B · h
cm
2
? cm ? cm
3
Great job!
You just found that the area of the base is 36 cm
2
. Find the height of the prism, and then determine the volume.
3D shape with pentagonal base composed of a rectangle with side lengths 4 cm by 6 cm, and a triangle atop the 6 cm length of the rectangle. The triangle is labeled with height 4 cm, and a side length of 3 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B · h
36 cm
2
cm
cm
3
Answers
GPT-4o mini
To find the volume of the prism, we need to know both the area of the base and the height of the prism.
You’ve already determined the area of the base (B) to be 36 cm². Now, let’s find the height (h) of the prism.
From the description, it seems the height of the prism corresponds to the height of the rectangular portion of the base. If this isn’t specifically stated, the height of the prism would generally be given, or you would be looking at the vertical height of the entire prism.
Assuming the prism has a vertical height that connects to the pentagonal shape described, it appears the essential height for calculating the volume would be the height of the prism itself. However, this specific value was not provided.
**Finding the Height:**
If we assume that the triangular section with a height of 4 cm connects the two bases, this directly contributes to the overall height of the prism.
For the sake of calculation, let's assume that the height of the prism **h = 4 cm** (the height of the triangle, as commonly the prism height is the same as the height of the triangular component in this configuration).
**Volume Calculation:**
Now that we have:
- Area of the base (B) = 36 cm²
- Height of the prism (h) = 4 cm
We can calculate the volume (V) using the formula:
\[
V = B \cdot h
\]
Substituting the values in:
\[
V = 36 \, \text{cm}^2 \cdot 4 \, \text{cm}
\]
\[
V = 144 \, \text{cm}^3
\]
So, the volume of the prism is **144 cm³**.
You’ve already determined the area of the base (B) to be 36 cm². Now, let’s find the height (h) of the prism.
From the description, it seems the height of the prism corresponds to the height of the rectangular portion of the base. If this isn’t specifically stated, the height of the prism would generally be given, or you would be looking at the vertical height of the entire prism.
Assuming the prism has a vertical height that connects to the pentagonal shape described, it appears the essential height for calculating the volume would be the height of the prism itself. However, this specific value was not provided.
**Finding the Height:**
If we assume that the triangular section with a height of 4 cm connects the two bases, this directly contributes to the overall height of the prism.
For the sake of calculation, let's assume that the height of the prism **h = 4 cm** (the height of the triangle, as commonly the prism height is the same as the height of the triangular component in this configuration).
**Volume Calculation:**
Now that we have:
- Area of the base (B) = 36 cm²
- Height of the prism (h) = 4 cm
We can calculate the volume (V) using the formula:
\[
V = B \cdot h
\]
Substituting the values in:
\[
V = 36 \, \text{cm}^2 \cdot 4 \, \text{cm}
\]
\[
V = 144 \, \text{cm}^3
\]
So, the volume of the prism is **144 cm³**.