Question

A pyramid with height 15 is separated into two pieces by a plane parallel to the base and 6 units above it. What is the positive difference in the volumes of these two pieces if the volume of the original pyramid is 250 cubic units?

Answer 1

I feel like I'm answering my own questions now, but I'm getting 196. How about the rest of you?

Answer 2

Vol = 1/3 b h. Right?
Original height is 15 and small one's height is 6.
And base sides should be in the same proportion (2/5)
So I'd say the volume of the small one should be (2/5)^3 times volume of the large one. Is that right?

Answer 3

the top is similar to the whole, with height 15-6=9
so
9^2/ 15^2 = x/250
to find the vol of the top
we can then find the bottom, and the difference

Answer 4

Wait, don't you have to divide 250 by 15 first to get the area of a base?

Answer 5

Oh and multiply by 3?

Answer 6

amend that to
9^3/ 15^3 = x/250

Answer 7

I think so.

Answer 8

I am getting 54 for that and once you subtract it, you get 196?

Answer 9

That's what I get too.

Answer 10

But I just checked the answer key, and it says that it's 142

Answer 11

the top is 54 , the bottom is 250- 54= 196
the difference between the two is 196-54= 142

Answer 12

Wait, why would you subtract twice?

Answer 13

Wouldn't 54 be the volume of one piece and 250 the other?

Answer 14

the question is asking for the difference between the vol of the top piece and the bottom piece.

Answer 15

250 is the entire pyramid

Answer 16

Oh! I just misread it...now I understand...thank you!