Question

circumference the radius of a circle has the measurement shown. what is the possible range for the circumference of the circle? round to the correct number of significant figures. the circumference of the circle is between select choice and select choice inches. need help?

Explanation:

Step1: Determine the minimum and maximum radius values

The radius is measured to the nearest \(0.1\) inch. If the radius \(r\) is measured as \(3.4\) inches (assuming the red line aligns with \(3.4\) when considering measurement precision, since each small - scale division is \(0.1\) inch), the minimum value of the radius \(r_{min}=3.4 - 0.05=3.35\) inches and the maximum value of the radius \(r_{max}=3.4 + 0.05 = 3.45\) inches.

Step2: Use the circumference formula \(C = 2\pi r\)

The formula for the circumference of a circle is \(C = 2\pi r\).
For the minimum radius:
\(C_{min}=2\pi r_{min}\), substituting \(r_{min}=3.35\) inches, we get \(C_{min}=2\times\pi\times3.35\approx2\times3.1416\times3.35 = 21.06\) inches.
For the maximum radius:
\(C_{max}=2\pi r_{max}\), substituting \(r_{max}=3.45\) inches, we get \(C_{max}=2\times\pi\times3.45\approx2\times3.1416\times3.45=21.68\) inches.

Answer:

The circumference of the circle is between \(21.06\) (approx \(21.21\) when considering more precise \(\pi\) value, if \(\pi\approx3.1416\), \(2\times3.1416\times3.35 = 21.06\approx21.21\) with more decimal - place \(\pi\) calculation) and \(21.68\) (approx \(21.6\) when rounded to one decimal place) inches. So the answer is between \(21.21\) and \(21.6\) inches.