Question

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

Answer 1

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

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: $V= (\frac{ a^{2}(3)h }{3} )$ 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!