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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

5 answers

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.

wrong , try again

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!

that is not it

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 \( 69.1875 \times 22.3 \):

\[ 69.1875 \times 22.3 = 1547.6875 \]

  1. 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!