Question

question 4 of 9
find the area of a circle with diameter 27.2 m, both in terms of \\(\pi\\) and to the nearest tenth. use 3.14 for \\(\pi\\).
\\(\bigcirc\\) \\(a = 54.4\pi\\,\text{m}^2 \approx 170.8\\,\text{m}^2\\)
\\(\bigcirc\\) \\(a = 184.96\pi\\,\text{m}^2 \approx 580.8\\,\text{m}^2\\)
\\(\bigcirc\\) \\(a = 27.2\pi\\,\text{m}^2 \approx 85.4\\,\text{m}^2\\)
\\(\bigcirc\\) \\(a = 739.84\pi\\,\text{m}^2 \approx 2323.1\\,\text{m}^2\\)

Explanation:

Step1: Find the radius

The diameter \( d = 27.2 \) m, so the radius \( r=\frac{d}{2}=\frac{27.2}{2} = 13.6 \) m.

Step2: Calculate area in terms of \( \pi \)

The formula for the area of a circle is \( A=\pi r^{2} \). Substitute \( r = 13.6 \):
\( A=\pi\times(13.6)^{2}=\pi\times184.96 = 184.96\pi \) \( m^{2} \).

Step3: Calculate the numerical value

Use \( \pi = 3.14 \), so \( A = 184.96\times3.14 \).
\( 184.96\times3.14=184.96\times3 + 184.96\times0.14=554.88+25.8944 = 580.7744 \approx 580.8 \) \( m^{2} \).

Answer:

A = 184.96π m² ≈ 580.8 m² (the option: A = 184.96π m² ≈ 580.8 m²)