Geometry - How to find the angle of a sector

A sector in a circle with a radius of has an area of $\frac{1}{4}\pi$ . In degrees, what is the measurement of the central angle of the sector?

$5.625^\circ$

$2.775^\circ$

$6.225^\circ$

$8.555^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times \frac{1}{4}\pi}{\pi\times 4^2}=\frac{90\pi}{16\pi}=5.625$

The central angle is degrees.

A sector in a circle with a radius of has an area of $12\pi$ . In degrees, what is the measurement of the central angle for this sector?

$30^\circ$

$45^\circ$

$60^\circ$

$15^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times12\pi}{\pi\times 12^2}=\frac{4320\pi}{144\pi}=30$

The central angle is degrees.

What is the sector angle, in degrees, if the area of the sector is $4\pi$ with a given radius of ?

$90^{\circ}$

$0^{\circ}$

$45^{\circ}$

$360^{\circ}$

$60^{\circ}$

Explanation

Write the formula for the area of a circular sector.

$A= \frac{\Theta }{360}\pi r^2$

Substitute the given information and solve for theta:

$4\pi= \frac{\Theta }{360}\pi (4)^2$

$\frac{1}{4}= \frac{\Theta }{360}$

$\Theta= \frac{360}{4} = 90^{\circ}$

A sector in a circle with a radius of has an area of $12\pi$ . In degrees, what is the measurement of the central angle of the sector?

$270^\circ$

$285^\circ$

$255^\circ$

$240^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times12\pi}{\pi\times 4^2}=\frac{4320\pi}{16\pi}=270$

The central angle is degrees.

A sector in a circle with a radius of has an area of $14\pi$ . In degrees, what is the measurement of the central angle of the sector?

$140^\circ$

$150^\circ$

$130^\circ$

$120^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 14\pi}{\pi\times 6^2}=\frac{5040\pi}{36\pi}=140$

The central angle is degrees.

A sector in a circle with a radius of has an area of $\pi$ . In degrees, what is the measurement of the central angle of the sector?

$10^\circ$

$5^\circ$

$15^\circ$

$20^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times \pi}{\pi\times 6^2}=\frac{360\pi}{36\pi}=10$

The central angle is degrees.

A sector in a circle with a radius of has an area of $35\pi$ . In degrees, what is the measurement of the central angle of the sector?

$350^\circ$

$340^\circ$

$330^\circ$

$320^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 35\pi}{\pi\times 6^2}=\frac{12600\pi}{36\pi}=350$

The central angle is degrees.

A sector in a circle with a radius of has and area of $34\pi$ . In degrees, what is the measurement of the central angle of the sector?

$340^\circ$

$350^\circ$

$345^\circ$

$355^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 34\pi}{\pi\times 6^2}=\frac{12240\pi}{36\pi}=340$

The central angle is degrees.

A sector in a circle with a radius of has an area of $2\pi$ . In degrees, what is the measurement of the central angle in the sector?

$28.8^\circ$

$30.2^\circ$

$32.6^\circ$

$34.8^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 2\pi}{\pi\times 5^2}=\frac{720\pi}{25\pi}=28.8$

The central angle is degrees.

A sector in a circle with a radius of has an area of $60\pi$ . In degrees, what is the measurement of the central angle of the sector?

$337.5^\circ$

$355.5^\circ$

$332.5^\circ$

$305.5^\circ$

Explanation

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 60\pi}{\pi\times 8^2}=\frac{21600\pi}{64\pi}=337.5$

The central angle is degrees.

How to find the angle of a sector

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