Question
Volume of Pyramids Practice
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Question
A right rectangular pyramid has an altitude of 22.3 inches, a length of 6.75 inches, and a width of 10.25 inches. What is the volume of the pyramid in cubic inches?(1 point)
in.3
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
A right rectangular pyramid has an altitude of 22.3 inches, a length of 6.75 inches, and a width of 10.25 inches. What is the volume of the pyramid in cubic inches?(1 point)
in.3
Answers
GPT-4o mini
To calculate the volume of a right rectangular pyramid, you can use the formula:
\[
V = \frac{1}{3} \times B \times h
\]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height (or altitude) of the pyramid.
1. First, calculate the area of the base \( B \):
- The area \( B \) of the rectangular base is given by the formula:
\[
B = \text{length} \times \text{width} = 6.75 \, \text{inches} \times 10.25 \, \text{inches}
\]
Calculating that gives:
\[
B = 6.75 \times 10.25 = 69.1875 \, \text{square inches}
\]
2. Now, substitute the area of the base and the height into the volume formula:
- The altitude (height) \( h \) is given as 22.3 inches.
\[
V = \frac{1}{3} \times 69.1875 \times 22.3
\]
Calculating \( V \):
\[
V = \frac{1}{3} \times 69.1875 \times 22.3 \approx \frac{1}{3} \times 1547.6875 \approx 515.8958333
\]
Rounding this to a reasonable number of decimal places (typically two for volume):
\[
V \approx 515.90 \, \text{cubic inches}
\]
Therefore, the volume of the pyramid is approximately **515.90 cubic inches**.
\[
V = \frac{1}{3} \times B \times h
\]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height (or altitude) of the pyramid.
1. First, calculate the area of the base \( B \):
- The area \( B \) of the rectangular base is given by the formula:
\[
B = \text{length} \times \text{width} = 6.75 \, \text{inches} \times 10.25 \, \text{inches}
\]
Calculating that gives:
\[
B = 6.75 \times 10.25 = 69.1875 \, \text{square inches}
\]
2. Now, substitute the area of the base and the height into the volume formula:
- The altitude (height) \( h \) is given as 22.3 inches.
\[
V = \frac{1}{3} \times 69.1875 \times 22.3
\]
Calculating \( V \):
\[
V = \frac{1}{3} \times 69.1875 \times 22.3 \approx \frac{1}{3} \times 1547.6875 \approx 515.8958333
\]
Rounding this to a reasonable number of decimal places (typically two for volume):
\[
V \approx 515.90 \, \text{cubic inches}
\]
Therefore, the volume of the pyramid is approximately **515.90 cubic inches**.
wrong , try again
GPT-4o mini
Let’s go through the calculations step by step again to ensure accuracy when calculating the volume of the pyramid.
The formula for the volume \( V \) of a right rectangular pyramid is:
\[
V = \frac{1}{3} \times B \times h
\]
where:
- \( B \) is the area of the base, and
- \( h \) is the height (altitude) of the pyramid.
### Step 1: Calculate the area of the base \( B \)
The base of the pyramid is a rectangle. The area \( B \) can be calculated as:
\[
B = \text{length} \times \text{width}
\]
Given:
- Length = 6.75 inches
- Width = 10.25 inches
Calculating the area:
\[
B = 6.75 \times 10.25 = 69.1875 \, \text{square inches}
\]
### Step 2: Substitute into the volume formula
Now, plug the area \( B \) and the height \( h \) into the volume formula. The given height \( h \) is 22.3 inches:
\[
V = \frac{1}{3} \times 69.1875 \times 22.3
\]
### Step 3: Perform the calculations
First, multiply the area of the base \( B \) by the height \( h \):
\[
69.1875 \times 22.3 \approx 1546.6875
\]
Now, divide by 3 to find the volume:
\[
V = \frac{1546.6875}{3} \approx 515.5625
\]
### Final Result
Thus, the volume of the pyramid is approximately:
\[
V \approx 515.56 \, \text{cubic inches}
\]
If you would like this rounded to two decimal places, it would be:
\[
\boxed{515.56 \, \text{cubic inches}}
\]
Please let me know if you'd like to go through any other questions or if there's something specific you'd like to clarify!
The formula for the volume \( V \) of a right rectangular pyramid is:
\[
V = \frac{1}{3} \times B \times h
\]
where:
- \( B \) is the area of the base, and
- \( h \) is the height (altitude) of the pyramid.
### Step 1: Calculate the area of the base \( B \)
The base of the pyramid is a rectangle. The area \( B \) can be calculated as:
\[
B = \text{length} \times \text{width}
\]
Given:
- Length = 6.75 inches
- Width = 10.25 inches
Calculating the area:
\[
B = 6.75 \times 10.25 = 69.1875 \, \text{square inches}
\]
### Step 2: Substitute into the volume formula
Now, plug the area \( B \) and the height \( h \) into the volume formula. The given height \( h \) is 22.3 inches:
\[
V = \frac{1}{3} \times 69.1875 \times 22.3
\]
### Step 3: Perform the calculations
First, multiply the area of the base \( B \) by the height \( h \):
\[
69.1875 \times 22.3 \approx 1546.6875
\]
Now, divide by 3 to find the volume:
\[
V = \frac{1546.6875}{3} \approx 515.5625
\]
### Final Result
Thus, the volume of the pyramid is approximately:
\[
V \approx 515.56 \, \text{cubic inches}
\]
If you would like this rounded to two decimal places, it would be:
\[
\boxed{515.56 \, \text{cubic inches}}
\]
Please let me know if you'd like to go through any other questions or if there's something specific you'd like to clarify!
that is not it
GPT-4o mini
Let's re-evaluate the problem thoroughly to ensure the calculations are spot on.
The volume \( V \) of a right rectangular pyramid is given by the formula:
\[
V = \frac{1}{3} \times B \times h
\]
Where:
- \( B \) is the area of the base (which is a rectangle),
- \( h \) is the height of the pyramid.
### Step 1: Calculate the Area of the Base \( B \)
Given:
- Length = 6.75 inches
- Width = 10.25 inches
The area \( B \) of the rectangular base is calculated as:
\[
B = \text{length} \times \text{width} = 6.75 \, \text{inches} \times 10.25 \, \text{inches}
\]
Calculating that:
\[
B = 6.75 \times 10.25 = 69.1875 \, \text{square inches}
\]
### Step 2: Use the Height
The height of the pyramid \( h \) is given as 22.3 inches.
### Step 3: Plug Values into the Volume Formula
Substituting \( B \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \times 69.1875 \times 22.3
\]
Calculating the volume step-by-step:
1. Calculate \( 69.1875 \times 22.3 \):
\[
69.1875 \times 22.3 = 1547.6875
\]
2. Now divide by 3 to find the volume:
\[
V = \frac{1547.6875}{3} = 515.8958333
\]
### Final Result
Rounding to two decimal places, we find:
\[
V \approx 515.90 \, \text{cubic inches}
\]
Please let me know if there are any specifics that I may have misunderstood. The calculation for the volume is consistent, and 515.90 cubic inches should be correct based on the values provided. If there's a mistake in the values or expectations, please clarify!
The volume \( V \) of a right rectangular pyramid is given by the formula:
\[
V = \frac{1}{3} \times B \times h
\]
Where:
- \( B \) is the area of the base (which is a rectangle),
- \( h \) is the height of the pyramid.
### Step 1: Calculate the Area of the Base \( B \)
Given:
- Length = 6.75 inches
- Width = 10.25 inches
The area \( B \) of the rectangular base is calculated as:
\[
B = \text{length} \times \text{width} = 6.75 \, \text{inches} \times 10.25 \, \text{inches}
\]
Calculating that:
\[
B = 6.75 \times 10.25 = 69.1875 \, \text{square inches}
\]
### Step 2: Use the Height
The height of the pyramid \( h \) is given as 22.3 inches.
### Step 3: Plug Values into the Volume Formula
Substituting \( B \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \times 69.1875 \times 22.3
\]
Calculating the volume step-by-step:
1. Calculate \( 69.1875 \times 22.3 \):
\[
69.1875 \times 22.3 = 1547.6875
\]
2. Now divide by 3 to find the volume:
\[
V = \frac{1547.6875}{3} = 515.8958333
\]
### Final Result
Rounding to two decimal places, we find:
\[
V \approx 515.90 \, \text{cubic inches}
\]
Please let me know if there are any specifics that I may have misunderstood. The calculation for the volume is consistent, and 515.90 cubic inches should be correct based on the values provided. If there's a mistake in the values or expectations, please clarify!