Question

Can someone help me with this geometry question? It’s part C I will provide you with more information about the question if needed.

Answer 1

`V=(1)/(3)*\pi *r^2*h`

C)

1) For cones and pyramids, we're going to use this general formula:

`V=(1)/(3)*A_(base)*h`

2) And since the pyramid and the cone have the same height, we can find the common heigh they share by plugging into the Volume of pyramid formula the given height:

`\begin{gathered} V=(1)/(3)*Ab*h \\ (144)/(3)\pi h=(1)/(3)*Ab.h \\ (144)/(3)\pi h=(1)/(3)Abh \\ \end{gathered}`

Note that the base of a cone is a circumference, so we can replace that with the formula for the area of the circle:

`\begin{gathered} (144\pi)/(3)h=(1)/(3)*(\pi *r^2)*h \\ (144)/(3)\pi h=(\pi *r^2)/(3)*h \\ 3*(144)/(3)\pi h=(\pi r^(2))/(3)h*3 \\ r^2=144 \\ r=√(144) \\ r=12 \\ ---- \\ \end{gathered}`

3) Finally, let's test

`\begin{gathered} (144)/(3)\pi h=(1)/(3)\pi r^2*h \\ (144)/(3)\pi h=(1)/(3)\pi *12^2*h \\ (144)/(3)\pi h=(144)/(3)\pi h \\ \end{gathered}`

4) Thus the formula for the volume of a cone is:

`V=(1)/(3)*\pi *r^2*h`