[tex]h\text{ = }\frac{3V}{πr²}\text{ (option D)}[/tex]
Explanation:
[tex]\begin{gathered} \text{Volume of the cone = }\frac{1}{3}\pi r^{}^{2}h \\ h\text{ = height} \\ r\text{ = radius} \end{gathered}[/tex]
We need to make h the subject of formula:
[tex]\begin{gathered} All\text{ the variables on the right are multiplied together.} \\ \text{First we get rid of the 1/3 by multiplying both sides by 3:} \\ 3(V)\text{ =3( }\frac{1}{3}\pi r^{2}h) \\ 3V\text{ = }\pi r^{2}h \end{gathered}[/tex][tex]\begin{gathered} \text{For h to stand alone on the right side, we divide both sides by }\pi r^2h \\ We\text{ apply division beause all the variables were ultiplied together} \\ So\text{ to undo it, we divide} \\ \frac{3V}{\pi r^{2}}=\text{ }\frac{\pi r^{2}h}{\pi r^{2}} \\ \frac{3V}{\pi r^2}=\text{ }h \end{gathered}[/tex][tex]h\text{ = }\frac{3V}{\pi r^{2}}\text{ (option D)}[/tex]
