how to find area of a sector

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Circles, Sectors, Segments
Surface area Of Circles
More Geometry Lessons

The following table gives the formulas for the area of sector and area of segment for angles in degrees or radians. Scroll down the page for more explanations, examples and worksheets for the area of sectors and segments.

area of sector formula

Area Of Sector

A sector is like a "pizza slice" of the circle. Information technology consists of a region bounded by ii radii and an arc lying between the radii.

The area of a sector is a fraction of the area of the circle. This expanse is proportional to the central angle. In other words, the bigger the central angle, the larger is the expanse of the sector.

The following diagrams give the formulas for the surface area of circle and the area of sector. Scroll down the page for more examples and solutions.

Area of Circle and Sector

Formula For Area Of Sector (In Degrees)

We volition at present look at the formula for the area of a sector where the central angle is measured in degrees.

Recall that the angle of a full circumvolve is 360˚ and that the formula for the area of a circle is πr².

Comparing the area of sector and surface area of circumvolve, we derive the formula for the area of sector when the cardinal angle is given in degrees.

area sector formula
where r is the radius of the circumvolve.

This formula allows us to summate any one of the values given the other two values.

Worksheet to calculate arc length and area of a sector (degrees)

Calculate The Surface area Of A Sector (Using Formula In Degrees)

We can calculate the surface area of the sector, given the fundamental bending and radius of circumvolve.

Example:
Given that the radius of the circumvolve is five cm, summate the expanse of the shaded sector. (Take π = 3.142).

area of sector

Solution:

Expanse of sector = 60°/360° × 25π
= 13.09 cm^two

Calculate Central Angle Of A Sector

We can summate the central angle subtended by a sector, given the area of the sector and area of circle.

Example:
The surface area of a sector with a radius of 6 cm is 35.4 cm². Summate the angle of the sector. (Accept π = 3.142).

Solution:

Central Angle = 35.four/36π × 360°
= 112.67°

How To Derive The Formula To Calculate The Area Of A Sector In A Circumvolve?

It explains how to find the area of a sector of a circle. The formula for the area of a circle is given and the formula for the area of a sector of a circle is derived.

Instance:
Janice needs to find the expanse of the red section of the circular table top in club to buy the right corporeality of paint. What is the area of the reddish department of the round table top?

Solution:
Step 1: Find the area of the entire circle using the area formula A = πrⁱⁱ.
Step 2: Find the fraction of the circle by putting the angle measurement of the sector over 360°, the full number of degrees in a circle.
Step 3: Multiply the fraction by the area of the circle. Leave your answer in terms of π.

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How To Summate The Expanse Of A Sector Using The Formula In Degrees And The Missing Radius Given The Sector Expanse And The Size Of The Cardinal Angle?

Instance ane: Notice the area of the shaded region.

Example two: Find the radius of the circle if the area of the shaded region is 50π

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Formula For Surface area Of Sector (In Radians)

Next, we will await at the formula for the surface area of a sector where the key angle is measured in radians. Call up that the angle of a full circle in radians is 2π.

Comparing the surface area of sector and surface area of circumvolve, we get the formula for the surface area of sector when the cardinal angle is given in radians.

formula area sector
where r is the radius of the circumvolve.

This formula allows us to summate any one of the values given the other ii values.

Worksheet to summate arc length and area of sector (radians)

Summate The Area Of Sector (Using Formula In Radians)

The following video shows how we can calculate the area of a sector using the formula in radians.

Case:
A lawn sprinkler located at the corner of a yard rotates through xc° and sprays water 30ft. What is the area of the sector watered?

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How To Decide The Surface area Of A Sector?

The formula is given in radians.
How to decide the surface area of a segment? (the surface area bounded by a chord and an arc).

Case one: Find the expanse of the sector of a circumvolve with radius 8 feet formed past a central angle of 110°

Example 2: Find the area of the shaded region in the circle with radius 12cm and a cardinal bending of fourscore°.

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Area Of Segment (Bending In Degrees)

The segment of a circle is a region divisional by the arc of the circle and a chord.

The surface area of segment in a circle is equal to the expanse of sector minus the area of the triangle.

How To Derive The Expanse Of A Segment Formula?

How do you observe the area of a segment of a circumvolve?

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How To Calculate The Expanse Of Segments Of Circles?

It uses one-half the production of the base and the summit to calculate the area of the triangle.

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How To Calculate The Surface area Of Sector And The Area Of Segment?

It uses the sine rule to calculate the area of triangle.

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Area Of Segment (Angle In Radians)

Finding the area of a segment (angle given in radians)

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