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Flashcards: Common Core: High School - Geometry

Determine the area of the sector of a circle that has a central angle of 123 degrees and a circumference of .

Refer to the following figure to help calculate the solution.

Circlearc5 6

$\text{sector area}= 6.89$

$\text{sector area}= 6.96$

$\text{sector area}= 6.98$

$\text{sector area}= 7.16$

$\text{sector area}= 6.69$

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Flashcards: Common Core: High School - Geometry

Determine the area of the sector of a circle that has a central angle of 123 degrees and a circumference of .

Refer to the following figure to help calculate the solution.

Circlearc5 6

Your answer:

$\text{sector area}= 6.89$

Your answer:

$\text{sector area}= 6.98$

Your answer:

$\text{sector area}= 7.16$

Your answer:

$\text{sector area}= 6.69$

Correct answer:

$\text{sector area}= 6.96$

Explanation:

To calculate the area of the sector of the circle all that is needed is the central angle and the area of the circle. Since the central angle and circumference are given the area of the circle can be calculated.

The formulas to find the area and circumference of a circle are as follows.

$\\A=\pi r^2 \\C=2\pi r$

The known information is,

$\\\theta =123^\circ \\C=16$

Solving for the radius,

$\\16=2\pi r \\8=\pi r \\\\r=\frac{8}{\pi}$

Now the area of the whole circle is,

$\\A=\pi r^2 \\A=\pi \left(\frac{8}{\pi} \right )^2 \\\\A=\pi \times \frac{64}{\pi^2} \\\\A=\frac{64}{\pi}$

Now, since the question is asking for the area of the sector, a ratio will need to be constructed. Recall that a circle is composed of 360 degrees. Therefore, the following ratio can be made,

$\\\frac{\theta}{360^\circ}=\frac{\text{sector area}}{\frac{64}{\pi}} \\\\\frac{123^\circ}{360^\circ}=\frac{\text{sector area}}{\frac{64}{\pi}} \\\\\frac{41}{120}=\frac{\text{sector area}}{\frac{64}{\pi}} \\\\\frac{41}{120}\times \frac{64}{\pi}=\text{sector area} \\\\\text{sector area}=6.96$

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All Common Core: High School - Geometry Resources

Flashcards: Common Core: High School - Geometry

Flashcards: Common Core: High School - Geometry

Flashcards: Common Core: High School - Geometry

Flashcards: Common Core: High School - Geometry

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