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.

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

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:
[tex]3V= a^{2} h[/tex]

So, we are looking to see which of the choices given produces a volume equal to [tex] a^{2} h[/tex].

The first choice is the right answer. Notice what happens when we take the volume formula and multiply the h by 3. We get: [tex]V= (\frac{ a^{2}(3)h }{3} ) [/tex] 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 [tex] a^{2} h[/tex] which is what we were looking for!