Math word problem, I need help?

I'm going to try to explain this as simply as possible!

A rectangular prism's volume is calculated by multiplying the base area by the height, or v = b*h.

The base area is calculated by multiplying the length and the width, or a = l*w.

Now, just ignore all of that and remember that the volume of a rectangular prism is calculated the same way as the volume of any cube, which is length * width * height, or v = l*w*h.

So, if you add any number (represented by "k" in your question) to all three sides, the volume will be increased by k^3.

Look at it this way:

v = l * w * h

v = (l+k) * (w+k) * (h+k)

Can you see that this is the same as v = l*w*h + k*k*k, or v = l*w*h + k^3?

And that the volume increased by k^3?

I hope so, because I'm sometimes not that great at explaining things!

Now, in the case of a pyramidal prism, the volume is equal to the base area times (height divided by 3), or v = l*w * (1/3 * h).

This means that if you add "k" to all three measurements, you would get this:

v = (l + k) * (w + k) * (1/3)(h + k), or v =( l*w + k^2) (h/3 + k/3)

...which is definitely not equal to adding k^3 to the original volume.

Basically, the volume of the pyramidal prism is increasing by k^2 * k/3.

This is your answer and your explanation, though you may not have to go into this much detail-- I'm not sure what level your class involves.

In simpler terms: No, because the length and width of the pyramidal prism each increase by k, but the height/3 increases by only k/3.