Calculate the area of a sector of a circle with radius $ r $ and central angle $ heta $ (in radians)

The area of a sector of a circle with radius $ r $ and central angle $ \theta $ can be calculated using the formula:

$ A = \frac{1}{2} r^2 \theta $

For example, if $ r = 5 $ and $ \theta = \frac{\pi}{3} $:

$ A = \frac{1}{2} \cdot 5^2 \cdot \frac{\pi}{3} = \frac{25 \pi}{6} $

So, the area is $ \frac{25 \pi}{6} $ square units.

The area of a sector of a circle with radius $ r $ and central angle $ heta $ is given by:

$ A = frac{1}{2} r^2 heta $

For example, if $ r = 3 $ and $ heta = frac{pi}{4} $:

$ A = frac{1}{2} cdot 3^2 cdot frac{pi}{4} = frac{9 pi}{8} $

Therefore, the area is $ frac{9 pi}{8} $ square units.

The area of a sector of a circle is:

$ A = frac{1}{2} r^2 heta $

If $ r = 4 $ and $ heta = frac{pi}{2} $:

$ A = frac{1}{2} cdot 4^2 cdot frac{pi}{2} = 4 pi $

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