SOLUTION: Please help with this question: A pyramid has a rectangular base. Suppose that the edges of the base and the height of the pyramid are all doubled in length. What happens to the v

Algebra ->  Volume -> SOLUTION: Please help with this question: A pyramid has a rectangular base. Suppose that the edges of the base and the height of the pyramid are all doubled in length. What happens to the v      Log On


   

Question 467008: Please help with this question:
A pyramid has a rectangular base. Suppose that the edges of the base and the height of the pyramid are all doubled in length. What happens to the volume?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the volume of a rectangular pyramid:
V+=+%281%2F3%29B%2Ah Where B = area of the base of the pyramid (L*W) and h = its perpendicular height.
Let's say that the area of the base of the original pyramid is given by a%2Ab and its height is h. Its volume is then:
highlight%28V%5B1%5D+=+%281%2F3%29abh%29
Now we'll double the three dimensions to 2a, 2b, and 2h and find the new volume:
V%5B2%5D+=+%281%2F3%29%282a%29%282b%29%282h%29 Simplifying this we get:
highlight_green%28V%5B2%5D+=+%281%2F3%29%288%29abh%29
As you can see, the new volume is 8 times the original volume.