Question

synthesis

1. describe a strategy for determining an unknown dimension of a cylinder or cone.

use the examples if they help with your thinking.

Explanation:

1. Identify the known values: First, list out all given measurements (like volume, radius, height) and the unknown dimension you need to find.
2. Select the correct formula: Choose the volume formula for the shape:

• Cylinder: $V=\pi r^2 h$
• Cone: $V=\frac{1}{3}\pi r^2 h$

(Where $V$ = volume, $r$ = base radius, $h$ = height)

1. Rearrange the formula: Isolate the unknown dimension on one side of the equation using algebraic manipulation.
2. Substitute and calculate: Plug the known values into the rearranged formula and compute the unknown dimension.

Example for a cylinder: If $V=150\pi$ and $r=5$, find $h$.
Rearrange $V=\pi r^2 h$ to $h=\frac{V}{\pi r^2}$, then substitute: $h=\frac{150\pi}{\pi (5)^2}=\frac{150}{25}=6$.

Example for a cone: If $V=40\pi$ and $h=10$, find $r$.
Rearrange $V=\frac{1}{3}\pi r^2 h$ to $r^2=\frac{3V}{\pi h}$, then substitute: $r^2=\frac{3(40\pi)}{\pi (10)}=12$, so $r=\sqrt{12}=2\sqrt{3}$.

Answer:

1. List known values and the unknown dimension.
2. Choose the correct volume formula for the shape.
3. Rearrange the formula to isolate the unknown.
4. Substitute known values and solve for the unknown dimension.