Question

A cylinder is shown below. A cone with the same base as the cylinder is drawn inside the cylinder, and the vertex of the cone is on the opposite base of the cylinder.

Part A
What is the ratio of the volume of the cone to the volume of the cylinder?
-1:2
-2:1
-1:3
-3:1

Part B
If the volume of the cone is 126 cubic units, what is the volume of the cylinder?
-504
-252
-756
-378

Answer 1

A)

first off, let's take a peek at the volume for each, a cone and a cylinder

`\begin{array}{llll} \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height \end{cases} \end{array}\hspace{5em} \begin{array}{llll} \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height \end{cases} \end{array}`

notice, the cone's volume is just the same as cylinder over 3, or namely 1/3 that of a cylinder's, so

`\cfrac{\stackrel{cone}{volume}}{\underset{cylinder}{volume}}\implies \cfrac{1}{3}\implies 1~~ : ~~3`

B)

well, if the cone has a volume of 126, the cylinder will be 3 times that much or 378, assuming the radius and height is the same for both.