# Question #e85fa

Oct 20, 2015

Find the height of the pyramid, then solve the problem.

#### Explanation:

Here is a sketch of the problem:

Let's label the distance $E Z = j$

Using the law of similar triangles :

$\frac{5}{3.18 + j} = \frac{2}{j}$

solving for j:

$5 j = 2 \left(3.18 + j\right)$ or $j = 2.12$

So, now we know the distance $E Z = 2.12$

We also now know the height of the pyramid:

height $= Y Z = 3.18 + 2.12 = 5.3$

Volume of Pyramid $= \left(\frac{1}{3}\right) B h = \left(\frac{1}{3}\right) 25 \cdot 5.3$

Volume of small Pyramid $= \left(\frac{1}{3}\right) 4 \cdot 2.12$

Volume of Fulcrum $= \left(\frac{1}{3}\right) 25 \cdot 5.3 - \left(\frac{1}{3}\right) 4 \cdot 2.12$

Ratio $= \frac{\left(\frac{1}{3}\right) 25 \cdot 5.3 - \left(\frac{1}{3}\right) 4 \cdot 2.12}{\left(\frac{1}{3}\right) 25 \cdot 5.3} = \frac{117}{125}$

hope that helped