Question

5. Which equation is solved for the height of the cone based on theinformation given below?The equation V = 1 r represents the volume of a cone, where is the radius of the cone andh is the height of the coneh=V - Tr?h= } #r?VB3V - #r2 = h3Vha?D

Answer 1

`h\text{ = }(3V)/(πr²)\text{ (option D)}`

Step-by-step explanation:

`\begin{gathered} \text{Volume of the cone = }(1)/(3)\pi r^{}^(2)h \\ h\text{ = height} \\ r\text{ = radius} \end{gathered}`

We need to make h the subject of formula:

`\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( }(1)/(3)\pi r^(2)h) \\ 3V\text{ = }\pi r^(2)h \end{gathered}`
`\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} \\ (3V)/(\pi r^(2))=\text{ }(\pi r^(2)h)/(\pi r^(2)) \\ (3V)/(\pi r^2)=\text{ }h \end{gathered}`
`h\text{ = }(3V)/(\pi r^(2))\text{ (option D)}`