Question

If the height of a pyramid is cut in half what happens to the volume of the pyramid

Answer 1

`\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=base\\ h=height\\ -------\\ h=(h)/(2) \end{cases}\implies V=\cfrac{1}{3}B\cdot \cfrac{h}{2}`

what would you get for the fraction, simplified? does it say 1/3? does it change?

Answer 2

The formula for the volume of a pyramid is:


`Volume=(length*width*height)/(3)`

Let's pretend that we have a pyramid with a length of 3 and a width of 3 and a height of 6. If we plug this into the formula, we get


`V= (3*3*6)/(3) =18`

Now, let's pretend the height is 3.


`V= (3*3*3)/(3) =9`

9 is half of 18. This works for any numbers you plug in. If you half the height, than the volume is also halved.