Suppose a similar rectangular pyramid to the one shown has a scale factor of 3 . What would be the volume of the new pyramid?

Question

(1 point)
O 2, 190.22 ft.3
O 3, 285.33 ft.3
O 1,460.15 ft.3
• 182.52 ft.3

Answer 1

To find the volume of a rectangular pyramid with a scale factor of 3, we can use the fact that the volume of similar solids changes with the cube of the scale factor.

If \( V \) is the volume of the original pyramid, the volume \( V' \) of the new pyramid with the scale factor \( k \) (in this case, \( k = 3 \)) can be calculated using the formula:

\[ V' = k^3 \times V = 3^3 \times V = 27 \times V \]

Since we don't have the volume of the original pyramid provided in the question, we can't calculate the new volume directly. However, you can find the original volume, multiply it by 27, and choose the correct option from the answers provided based on that calculation.

If you have the original volume, please share it, and I can assist you further in calculating the new pyramid's volume. If you assume any of the options given is the original volume, you can find the new volume based on that.

Answer 2

28 22 24

Answer 3

It seems like you provided a set of numbers: 28, 22, and 24. It is unclear whether these represent the dimensions of the original rectangular pyramid or if you want to perform a different calculation.

To calculate the volume of a rectangular pyramid, you use the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

If 28, 22, and 24 are the dimensions of the base and height of the original pyramid, please clarify which two (if you mean for example, length and width of the base) are the base dimensions and which one is the height.

Assuming:

• Length (base) = 28
• Width (base) = 22
• Height = 24

We can calculate the volume of the original pyramid as follows:

1. Calculate the base area: \[ \text{Base Area} = 28 \times 22 = 616 , \text{ft}^2 \]

2. Calculate the volume: \[ V = \frac{1}{3} \times 616 \times 24 = \frac{14784}{3} = 4928 , \text{ft}^3 \]

Now, multiply this volume by the scale factor cubed to find the volume of the new pyramid.

\[ V' = 27 \times 4928 = 133056 , \text{ft}^3 \]

However, this result far exceeds the options you provided earlier. It might indicate a misunderstanding of the dimensions or what they represent.

Could you please clarify the dimensions or context? If those numbers represent something else (like the existing volume or something else), please specify that as well.