How To Find The Area Of A Sector Formula

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Sometimes you might need to decide the area of a sector, say for math questions or for a projection you are working on. A sector is a part of a circle that is shaped like a piece of pizza or pie. To find the area of this piece, you need to know the radius, arc length and the caste of the primal bending. With this information, finding the area of a sector is a simple matter of plugging the numbers into given formulas.

1
Gear up upwardly the formula $A=\left({\frac {\theta }{360}}\correct)\pi r^{2}$ . In the formula, r = the length of the radius, and θ "Theta" = the degrees in the central bending of the sector.^[1]
- Remember, the area of a circumvolve is $\pi r^{2}$ . When finding the surface area of a sector, you are really but calculating the area of the whole circumvolve, and and then multiplying past the fraction of the circle the sector represents.
- A circumvolve is 360 degrees, so when you place the measurement of the sector'south key bending over 360, it gives you the fraction of the whole circle.^[2]
2
Plug the sector's central angle measurement into the formula. Split the fundamental angle by 360. Doing this will give you what fraction or percent of the unabridged circle the sector represents.^[3]
- For example, if the central angle is 100 degrees, you will carve up 100 past 360, to get 0.28. (The area of the sector is about 28 per centum of the area of the whole circle.)
- If you don't know the measurement of the cardinal bending, only you lot know what fraction of the circle the sector is, determine the measurement of the angle by multiplying that fraction by 360. For instance, if you know the sector is one-fourth of the circle, multiply 360 by one-fourth (.25) to get 90 degrees.
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3
Plug the radius measurement into the formula. Square the radius, and multiply information technology by 𝝅 (iii.14). Doing this will permit you to calculate the area of the whole circle.^[4]
- For example, if the radius is five cm, you will square v to get 25, and so multiply 25 by 3.14, to get 78.v.
- If yous don't know the length of the radius, but yous know the diameter, merely divide the diameter by ii to notice the radius.
4
Multiply the two numbers together. Again, you will be multiplying the percent by the area of the whole circle. This gives you the area of the sector.
- For instance, 0.28 x 78.5 = 21.89.
- Since you are finding the area, the answer will be in square centimetres.
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Fix up the formula $A={\frac {rl}{2}}$ . In the formula, r = the length of the radius, and l = the length of the arc.
2
Plug in the arc length and radius into the formula. You will exist multiplying these two numbers to get a new numerator.^[six]
- For example, if the arc length is v cm and the radius is eight cm, your new numerator will be forty.
3
Split by ii. You are dividing the numerator found in footstep two. This gives you the area of the sector.
- For case, ${\frac {40}{2}}=20$ .
- Since you are finding the area, your answer will be in foursquare centimetres.
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Question

How do I find the surface area of a sector if I know the diameter and the arc length?

Divide the diameter past two. That gives you the radius. Multiply the radius by the arc length, then divide by 2 again. That gives you the sector area.
Question

How do I find the angle of a sector if I accept arch length and radius?

Double the radius, and then multiply past pi. That gives you the circumference. Carve up the length of the arc by the length of the circumference. That gives yous the fraction of the circumference represented by the arc. Multiply that fraction past 360°. That gives you the central angle of the sector.
Question

What is the area of a sector bounded by an arc of threescore degrees with a radius of iii feet?

Equally shown in a higher place, the formula is (60°/360°) π (three)² = (1/6)(3.14159)(ix). The expanse will exist expressed in foursquare feet.
Question

How practise I observe the area of a segment that does non accept degrees?

As indicated to a higher place, if you don't know the central angle, yous accept to know the radius and the arc length.
Question

How practice I find the expanse if I only know the radius?

You don't. The simply ii ways of finding a sector'south expanse are shown above.
Question

What is the central angle if the radius is 7 cm and the area of a sector is xv cm squared?

As shown in Method 1 higher up, the sector area equals the key bending divided by 360° and and so multiplied past πr². Therefore, the key angle is equal to the sector area multiplied by 360° and then divided by πr². In this example the angle is [(fifteen cm²)(360°)] / [(iii.14)(7² cm²)] = 35.1°.

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Article Summary X

To summate the area of a sector, start by finding the primal bending of the sector and dividing it by 360. Adjacent, take the radius, or length of 1 of the lines, square it, and multiply it by three.14. Then, multiply the two numbers to go the expanse of the sector. For example, if the fundamental bending is 100 degrees and the radius is five, you would divide 100 by 360 to get .28. And so, square 5 to get 25 before multiplying information technology by 3.14 for an answer of 78.5. Finally, multiply .28 by 78.5 for a terminal answer of 21.89, which is the area of the sector. To larn how to calculate the area of a sector if you don't know the cardinal angle, read on!

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