The volume of a square pyramid is V=1/3b^2h, where b is the length of one side of the base and h is the height of the pyramid. The length of each side of the base increases by 50%. Write a formula for the volume of the new pyramid.

Question

matt101 · Answer

The size of the new base increased by 50%, so it's 1.5 times the size of the old base. So, just use 1.5b instead of b in your equation for the volume of the pyramid and you'll have your answer! Remember it's squared!

anonymous · Answer

That doesn't make sense cause there is no previous pyramid though.

bibby · Answer

V=1/3b^2h is the original

anonymous · Answer

That's the equation I thought

matt101 · Answer

You just want a general formula for the new volume. That means you don't need to know what the actual volume was. The general formula for the starting volume is:

$$V={1 \over 3}b^2h$$
In our new pyramid, the base is 1.5 times greater. So the general formula for the volume of the new pyramid uses 1.5b instead of just b:

$$V={1 \over 3}(1.5b)^2h$$$$V=2.25 \times {1 \over 3}b^2h$$
So, you can see the new volume will be 2.25 times as large as the starting volume! Does that make sense?

anonymous · Answer

That makes sense now! Wow can't believe I didn't know how to do it. Thanks!