Question

b. complete the table showing how far this wheel travels for each number of rotations.

Explanation:

Step1: Find the distance per rotation

Since for \(2\) rotations the distance is \(140\pi\) cm.
The distance per rotation \(d=\frac{140\pi}{2}=70\pi\) cm.

Step2: Calculate distance for \(1\) rotation

For \(n = 1\) rotation, using the formula \(D=nd\) (where \(D\) is the total distance, \(n\) is the number of rotations and \(d\) is the distance per rotation).
\(D=1\times70\pi = 70\pi\) cm.

Step3: Calculate distance for \(10\) rotations

For \(n = 10\) rotations, using \(D=nd\).
\(D=10\times70\pi=700\pi\) cm.

Answer:

Number of Rotations	Distance (cm)
\(2\)	\(140\pi\)
\(5\)	\(350\pi\)
\(10\)	\(700\pi\)