Question

developing the area formula for circles

if \\(\overline{be}\\) measures 3.5 centimeters, the approximate area of circle b is square centimeters.

if \\(\overarc{ab}\\) measures 11 feet, the approximate area of circle b is square feet.

if \\(\overline{ef}\\) measures 12 meters, the approximate area of circle b is square meters.

Explanation:

First Sub - Question (BE = 3.5 cm)

Step1: Identify radius

BE is a radius (\(r\)) of circle B, so \(r = 3.5\) cm.

Step2: Use area formula

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = 3.5\) into the formula: \(A=\pi\times(3.5)^{2}\). Calculate \((3.5)^{2}=12.25\), then \(A=\pi\times12.25\approx3.14\times12.25 = 38.465\) square centimeters.

Second Sub - Question (AB = 11 ft)

Step1: Identify radius

AB is a radius (\(r\)) of circle B, so \(r = 11\) ft.

Step2: Use area formula

Using \(A=\pi r^{2}\), substitute \(r = 11\): \(A=\pi\times(11)^{2}=\pi\times121\approx3.14\times121 = 379.94\) square feet.

Third Sub - Question (EF = 12 m)

Step1: Identify diameter and radius

EF is a diameter (\(d\)) of circle B, so radius \(r=\frac{d}{2}=\frac{12}{2}=6\) m.

Step2: Use area formula

Using \(A = \pi r^{2}\), substitute \(r = 6\): \(A=\pi\times(6)^{2}=\pi\times36\approx3.14\times36=113.04\) square meters.

Answer:

• For \(BE = 3.5\) cm: \(\approx38.47\) (or 38.465) square centimeters.
• For \(AB = 11\) ft: \(\approx379.94\) square feet.
• For \(EF = 12\) m: \(\approx113.04\) square meters.