Question
Pentagonal prism B is the image of pentagonal prism A after dilation by a scale factor of 22. If the volume of pentagonal prism A is 56 incubed
3
, find the volume of pentagonal prism B, the image.
3
, find the volume of pentagonal prism B, the image.
Answers
GPT-4o mini
To find the volume of pentagonal prism B after dilation of pentagonal prism A, we can use the principle that when a shape is dilated by a scale factor \( k \), the volume of the shape is scaled by \( k^3 \).
Given:
- Volume of prism A \( V_A = 56 \) cubic units
- Scale factor \( k = 22 \)
The volume \( V_B \) of pentagonal prism B can be calculated using the following formula:
\[
V_B = k^3 \times V_A
\]
First, we calculate \( k^3 \):
\[
k^3 = 22^3 = 22 \times 22 \times 22 = 10648
\]
Now, we can find the volume of prism B:
\[
V_B = 10648 \times 56
\]
Calculating that gives:
\[
V_B = 596,288
\]
Therefore, the volume of pentagonal prism B is \( 596,288 \) cubic units.
Given:
- Volume of prism A \( V_A = 56 \) cubic units
- Scale factor \( k = 22 \)
The volume \( V_B \) of pentagonal prism B can be calculated using the following formula:
\[
V_B = k^3 \times V_A
\]
First, we calculate \( k^3 \):
\[
k^3 = 22^3 = 22 \times 22 \times 22 = 10648
\]
Now, we can find the volume of prism B:
\[
V_B = 10648 \times 56
\]
Calculating that gives:
\[
V_B = 596,288
\]
Therefore, the volume of pentagonal prism B is \( 596,288 \) cubic units.