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Answer :
Final answer:
To find the volume of pentagonal prism B, you multiply the volume of pentagonal prism A by the cube of the scale factor of 1/4. The volume of pentagonal prism B is therefore 128 cubic inches times 1/64, which equates to 2 cubic inches.
Explanation:
The question asks us to find the volume of pentagonal prism B, which is a dilation of pentagonal prism A by a scale factor of 1/4.
Since the scale factor relates to the linear dimensions of a shape, the corresponding change in volume will be the cube of the scale factor.
We start with the volume of pentagonal prism A being 128 cubic inches.
To calculate the volume of pentagonal prism B, we take the volume of A and multiply it by the scale factor cubed:
V(B) = V(A) × (scale factor)3
V(B) = 128 in3 × (1/4)3
V(B) = 128 in3 × 1/64
V(B) = 2 in3
Hence, the volume of pentagonal prism B is 2 cubic inches.
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