Question

9 what is the circumference of the circle shown below? write your answer in terms of π and rounded to the nearest hundredth in terms of π revisited

Explanation:

Step1: Recall circumference formula

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius of the circle.

Step2: Identify the radius

From the diagram, the radius \( r = 42 \) mm.

Step3: Substitute radius into formula

Substitute \( r = 42 \) into the formula \( C = 2\pi r \). So, \( C = 2\pi\times42 \).

Step4: Simplify the expression

\( 2\times42 = 84 \), so \( C = 84\pi \) mm. If we want a numerical approximation (rounded to the nearest hundredth), we know \( \pi\approx3.14159 \), so \( 84\pi\approx84\times3.14159 = 263.89356\approx263.89 \) mm. But the question asks for the answer in terms of \( \pi \) first, so the exact form in terms of \( \pi \) is \( 84\pi \) mm, and the approximate value is \( 263.89 \) mm.

Answer:

In terms of \( \pi \), the circumference is \( 84\pi \) millimeters. (If a numerical approximation is needed, it is approximately \( 263.89 \) millimeters.)