Question

In one revolution, how much farther does a point 10 cm from the center of the record travel than a point 3 cm from the center? Round your answer to the nearest tenth. INCLUDE A WRITTEN EXPLANATION OR HALF-CREDIT!

Answer 1

The distance that the point on the record travels can be calculated using the circumference formula:

`C=2\pi r`

The system described in the question can be drawn as shown below:

The circumference of Point A with a radius of 10 cm is calculated to be:

`\begin{gathered} C_A=2\pi*10 \\ C_A=20\pi\text{ cm} \end{gathered}`

The circumference of Point B with a radius of 3 cm is calculated to be:

`\begin{gathered} C_B=2\pi*3 \\ C_B=6\pi\text{ cm} \end{gathered}`

Therefore, the difference in distance is calculated to be:

`\Rightarrow20\pi-6\pi=14\pi=43.98\text{ cm}`

In decimals, to the nearest tenth, the answer will be 44.0 cm.