The distance that the point on the record travels can be calculated using the circumference formula:
[tex]C=2\pi r[/tex]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:
[tex]\begin{gathered} C_A=2\pi\times10 \\ C_A=20\pi\text{ cm} \end{gathered}[/tex]The circumference of Point B with a radius of 3 cm is calculated to be:
[tex]\begin{gathered} C_B=2\pi\times3 \\ C_B=6\pi\text{ cm} \end{gathered}[/tex]Therefore, the difference in distance is calculated to be:
[tex]\Rightarrow20\pi-6\pi=14\pi=43.98\text{ cm}[/tex]In decimals, to the nearest tenth, the answer will be 44.0 cm.
