How to make a similar shape thats half the volume?

Question

I have a rectangular prism that is 4 by 7 by 7 cm how do I make a similar shape that has half the volume

Answer

In general, volume varies as the cube of size. Half the volume corresponds to 0.7937 times the size. That is to say (0.7937)^3 = 1/2. So you multiply the given lengths by 0.7937.

Answer

The volume v of the rectangular prism is obviously 

v = 4 * 7 * 7 = 196.

You are looking for a prism of similar shape with half the volume:

v / 2 = (4 * 7 * 7) / 2 = 196 / 2 = 98.

As the condition is "similar shape", the ratio of the sides must not change. So the length of each side has to be multiplied by the same factor,  2^( -1/3) , which yields:

v / 2 = 4 / (2^(1/3)) * 7 / (2^(1/3)) * 7 / (2^(1/3)) = 98.

How to make a similar shape thats half the volume?

Answers (2)