SOLUTION: the length, width, and height of a rectangular prism are each cut in half. what is the ratio of the volume of the smaller prism to the volume of the larger prism?

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Question 1078981: the length, width, and height of a rectangular prism are each cut in half. what is the ratio of the volume of the smaller prism to the volume of the larger prism?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if the length is L, widthW , and height h, the volume of the larger prism is
V=L%2AW%2Ah
each cut in half, we have L%2F2, W%2F2, and h%2F2, so the volume of the smaler prism is V%5B1%5D=%28L%2F2%29%2A%28W%2F2%29%2A%28h%2F2%29
V%5B1%5D=%28L%2AW%2Ah%29%2F%282%2A2%2A2%29
than V%2FV%5B1%5D=%28L%2AW%2Ah%29%2F%28L%2AW%2Ah%29%2F8
V%2FV%5B1%5D=8%28cross%28L%2AW%2Ah%291%29%2F%28cross%28L%2AW%2Ah%291%29
V%2FV%5B1%5D=8%2F1
V%2A1=8%2AV%5B1%5D
V=8V%5B1%5D
the ratio of the volume of the smaller prism to the volume of the larger prism is 1to 8