Respuesta :
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!
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!