Question

Which of the following would triple the volume of the Egyptian square-based Pyramid below?

A. Multiply only the height by 3.

B. Add 3 to each dimension of the Pyramid.

C. Multiply every dimension of the Pyramid by 3.

D. Add 3 to the slant height.

Answer 1

The volume of a pyramid with a square base is given by:
`V= a^(2) ( (h)/(3))`. This is the way the volume is usually given but we can also multiply the two terms and write it this way:
`V= ( a^(2)h )/(3)`.

We are looking to triple the Volume which means we want to multiply it by 3. With respect to our volume equation, we multiply both sides by 3 to obtain:

`3V= a^(2) h`

So, we are looking to see which of the choices given produces a volume equal to
`a^(2) h`.

The first choice is the right answer. Notice what happens when we take the volume formula and multiply the h by 3. We get:
`V= (( a^(2)(3)h )/(3) )` and since there is a 3 in both the numerator (top) and the denominator (bottom) we can cross these out. That leaves us with a volume equal to
`a^(2) h` which is what we were looking for!