Answer:
(a). [tex]h=\frac{3V}{B}[/tex]
(b). 18 cm.
Step-by-step explanation:
We have been given the volume of pyramid is given by the formula [tex]V=\frac{1}{3}Bh[/tex], where B is the area of the base and h is the height.
(a). Let us solve the given formula for h as:
[tex]V=\frac{1}{3}Bh[/tex]
Multiply both sides by [tex]3[/tex]:
[tex]3\cdotV=3\cdot\frac{1}{3}Bh[/tex]
[tex]3V=Bh[/tex]
Divide both sides by B:
[tex]\frac{3V}{B}=\frac{Bh}{B}[/tex]
[tex]\frac{3V}{B}=h[/tex]
Switch sides:
[tex]h=\frac{3V}{B}[/tex]
(b). To find the height for the given pyramid, we will substitute the given values as:
[tex]h=\frac{3(216\text{ cm}^3)}{36\text{ cm}^2}[/tex]
[tex]h=\frac{648\text{ cm}}{36}[/tex]
[tex]h=18\text{ cm}[/tex]
Therefore, the height of the pyramid is 18 cm.
