A rectangular square pyramid has a base whose area is 25 sq. in. A section parallel to the base and 3.18 in. above it has an area of 4 sq. in. Find the ratio of the volume of the frustum to the volume of the pyramid?. (ans: 117:125)

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

Here is a sketch of the problem:

Let’s label the distance ##EZ = j##

Using the law of similar triangles :

##5/(3.18+j)=2/j##

solving for j:

##5j=2(3.18+j)## or ##j=2.12##

So, now we know the distance ##EZ = 2.12##

We also now know the height of the pyramid:

height ##=YZ=3.18+2.12=5.3##

Volume of Pyramid ##=(1/3)Bh=(1/3)25*5.3##

Volume of small Pyramid ##=(1/3)4*2.12##

Volume of Fulcrum ##=(1/3)25*5.3 – (1/3)4*2.12##

Ratio ##=[(1/3)25*5.3 – (1/3)4*2.12] / [(1/3)25*5.3] = 117/125##

hope that helped

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