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 L-shaped base labeled with side lengths in cm: 20, 5, 5, 15. A side length of 5 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B ยท h
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 L-shaped base labeled with side lengths in cm: 20, 5, 5, 15. A side length of 5 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B ยท h
cm
2
? cm ? cm
3
Answers
GPT-4o mini
To find the volume of the prism, we need to start with the area of the base. The base of the prism is L-shaped, and the dimensions provided are as follows:
- One long side is 20 cm.
- The other long side is 15 cm.
- The shorter sides of the 'L' are both 5 cm.
1. **Finding the area of the base (B)**:
The area of the L-shaped figure can be found by splitting it into two rectangles:
- Rectangle 1: The larger rectangle has dimensions 20 cm by 15 cm.
\[
\text{Area of Rectangle 1} = \text{length} \times \text{width} = 20 \, \text{cm} \times 15 \, \text{cm} = 300 \, \text{cm}^2
\]
- Rectangle 2: The smaller rectangle has dimensions 5 cm (width) by 5 cm (height).
\[
\text{Area of Rectangle 2} = \text{length} \times \text{width} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2
\]
Since Rectangle 2 is within Rectangle 1 (cut out), we need to subtract its area from the area of Rectangle 1:
\[
\text{Area of Base (B)} = \text{Area of Rectangle 1} - \text{Area of Rectangle 2} = 300 \, \text{cm}^2 - 25 \, \text{cm}^2 = 275 \, \text{cm}^2
\]
2. **Finding the height of the prism (h)**:
The height given is 5 cm.
3. **Calculating the volume (V)**:
Now that we have the area of the base and the height of the prism, we can calculate the volume using the formula:
\[
V = B \cdot h = 275 \, \text{cm}^2 \times 5 \, \text{cm} = 1375 \, \text{cm}^3
\]
Thus, the volume of the prism is:
\[
\boxed{1375 \, \text{cm}^3}
\]
- One long side is 20 cm.
- The other long side is 15 cm.
- The shorter sides of the 'L' are both 5 cm.
1. **Finding the area of the base (B)**:
The area of the L-shaped figure can be found by splitting it into two rectangles:
- Rectangle 1: The larger rectangle has dimensions 20 cm by 15 cm.
\[
\text{Area of Rectangle 1} = \text{length} \times \text{width} = 20 \, \text{cm} \times 15 \, \text{cm} = 300 \, \text{cm}^2
\]
- Rectangle 2: The smaller rectangle has dimensions 5 cm (width) by 5 cm (height).
\[
\text{Area of Rectangle 2} = \text{length} \times \text{width} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2
\]
Since Rectangle 2 is within Rectangle 1 (cut out), we need to subtract its area from the area of Rectangle 1:
\[
\text{Area of Base (B)} = \text{Area of Rectangle 1} - \text{Area of Rectangle 2} = 300 \, \text{cm}^2 - 25 \, \text{cm}^2 = 275 \, \text{cm}^2
\]
2. **Finding the height of the prism (h)**:
The height given is 5 cm.
3. **Calculating the volume (V)**:
Now that we have the area of the base and the height of the prism, we can calculate the volume using the formula:
\[
V = B \cdot h = 275 \, \text{cm}^2 \times 5 \, \text{cm} = 1375 \, \text{cm}^3
\]
Thus, the volume of the prism is:
\[
\boxed{1375 \, \text{cm}^3}
\]