The dimensions of a rectangular prism are multiplied by 1/2 (so the sides of the new rectangular prism will all be half). Describe the effect of change on the volume. a The volume will be multiplied by 1/8, 1/8 times as large. b The volume will be 1/2 as much. c The volume will be multiplied by 1/4, 1/4 times as large. d The volume will be twice as large.
Mathematics · College · Thu Feb 04 2021
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The correct answer is option a) The volume will be multiplied by 1/8, 1/8 times as large.
To understand the case, let's denote the dimensions of the original rectangular prism as length (l), width (w), and height (h). The volume (V) of a rectangular prism is calculated by multiplying these three dimensions together: V = l * w * h.
If each dimension of the rectangular prism is multiplied by 1/2, the new dimensions will be (1/2)l, (1/2)w, and (1/2)h. The new volume (V') will then be:
V' = (1/2)l * (1/2)w * (1/2)h V' = (1/2 * 1/2 * 1/2) * (l * w * h) V' = (1/8) * V
Thus, scaling all the dimensions of a rectangular prism by 1/2 results in the volume being scaled by 1/8 (since 1/2 cubed equals 1/8). The new volume is 1/8 times as large as the original volume.