Question:
In a circle with a radius of 10, what is the area of a sector with a central angle of 72 degrees?
In a circle with a radius of 10, what is the area of a sector with a central angle of 72 degrees?
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For sectors, the area is proportional to the fraction of the full circle, given by \( \frac{\theta}{360^\circ} \). Don't forget to square the radius when using the area formula.
Updated On: Oct 6, 2025
- \( 20\pi \)
- \( 25\pi \)
- \( 50\pi \)
- \( 100\pi \)
- \( 200\pi \)
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The Correct Option is B
Solution and Explanation
The formula for the area of a sector of a circle is:
\[
A = \frac{\theta}{360^\circ} \times \pi r^2,
\]
where \( \theta \) is the central angle (in degrees) and \( r \) is the radius of the circle.
We are given:
\[
r = 10
\text{and}
\theta = 72^\circ. \] Substitute these values into the formula for the area of the sector: \[ A = \frac{72}{360} \times \pi \times 10^2. \] Simplify the fraction \( \frac{72}{360} \): \[ \frac{72}{360} = \frac{1}{5}. \] Now, substitute this into the equation: \[ A = \frac{1}{5} \times \pi \times 100. \] Simplify further: \[ A = 20\pi. \] Thus, the area of the sector is \( \boxed{20\pi} \) square units.
\text{and}
\theta = 72^\circ. \] Substitute these values into the formula for the area of the sector: \[ A = \frac{72}{360} \times \pi \times 10^2. \] Simplify the fraction \( \frac{72}{360} \): \[ \frac{72}{360} = \frac{1}{5}. \] Now, substitute this into the equation: \[ A = \frac{1}{5} \times \pi \times 100. \] Simplify further: \[ A = 20\pi. \] Thus, the area of the sector is \( \boxed{20\pi} \) square units.
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