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# What is the area of a sector of a circle that has a diameter of 10 inches if the length of the arc is 10 inches?

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Top Answer
###### Answered 2009-08-02 02:54:01

The area of the full circle is (pi R2) = (25 pi) square inches. The full circumference is (2 pi R) = (10 pi) inches. An arc length of 10 is [ 10/(10 pi) ] = ( 1 / pi ) of the full circle. So the area of the sector is (full area / pi) = (25 pi) / pi = 25 square inches

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## Related Questions

The area of the sector of a circle which has a diameter of 10 inches if the length of the arc is 10 inches is: 25 square inches.

The area of a sector of a circle that has a diameter of ten inches if the length of the arc is ten inches is: 25 square units.

If you're only given the length of the arc, then you can't. You also need to know the fraction of the circle that's in the sector. You can figure that out if you know the angle of the arc, or the radius or diameter of the circle. -- Diameter of the circle = 2 x (radius of the circle) -- Circumference of the circle = (pi) x (Diameter of the circle) -- (length of the arc)/(circumference of the circle) = the fraction of the whole circle that's in the sector or -- (degrees in the arc)/360 = the fraction of the whole circle that's in the sector -- Area of the circle = (pi) x (radius of the circle)2 -- Area of the sector = (Area of the circle) x (fraction of the whole circle that's in the sector)

diameter d = 10 in radius r = 5 in arc length s = 10 in C = pi d = pi x 10 in = 10pi in s/C = 10 in/10pi in = 1/pi A circle = pi r2 = pi(5 in)2 = 25pi in2 A sector/A circle = 1/pi (cross multiply) pi A sector = 25pi in2 (divide both sides by pi) A sector = 25 in2

There is no direct relation between the area of a sector and the length of an arc. You must know the radius (or diameter) or the angle of the sector at the centre.

For a circle where sector measures 10 degrees and the diameter of the circle is 12: Sector area = 3.142 square units.

To calculate the arc length of a sector: calculate the circumference length, using (pi * diameter), then multiply by (sector angle / 360 degrees) so : (pi * diameter) * (sector angle / 360) = arc length

If you have the arc length:where:L is the arc length.R is the radius of the circle of which the sector is part.

25 square inches.Method:The area of complete circle is Pi x radius2 which is 3.14159 x 5 x 5, = 78.53982 sq ins.The circumference of a circle is Pi x diameter, which is 3.14159 x 10, = 31.4149 ins.But the arc is only 10/31.4159ths of the length of the full circle (10 divided by 31.4159 is 0.3183).So the area of sector with an arc 10 inches in length is: area of full circle (78.53982) x 0.3183 = 25.The above figures are only to a few significant decimal places. If you do the computations on a computer or a calculator the answer will come to exactly 25

The arc length of a sector that is 125 degrees and has a radius of 20 inches is: 43.63 inches.

The area of the sector of a circle with a radius of 2 inches and an arc of 60 degrees: 2.094 square inches.

Parts of a circle are:- Circumference Diameter Radius Chord Segment Sector Tangent

The answer depends on what information about the circle is given: area, radius, length and angle of arc, area and angle of sector, etc. In each case, there is a different way to calculate the diameter but, since there is no information on what is known, it is not possible to answer the question.

Geometrically, the parts of a circle are the diameter, radius, chord(s), circumference, arc, sector, segment, tangent, secant, the minor sector, and the major sector.

Divide the area of the sector by 360 and multiply it to the area. The area of the sector is 5 square inches.

The area of a sector of a circle with radius 12 and arc length 10pi is: 188.5 square units.

It depends on what information you have: the radius and the area of the sector or the length of the arc.

segment,tangent,radius,diameter,circumference,chord,semi-circle,center,arc and sector

The total central angle of the whole circle is 360 degrees. When the circle is divided into 20 equal sectors, each sector has a central angle of (360/20) = 18 degrees. The diameter of the circle is irrelevant. The answer is the same for diameters of 20 millimeters or 20 miles.

The area of the whole circle would have been &Iuml;&euro;*62 But instead of 360 degrees for the whole circle, the sector measures only 140 degrees. That is to say, the sector is 140/360 of the whole circle. Area = &Iuml;&euro;*62*140/360 = 43.9823 sq inches.

They are:- circumference diameter radius sector arc chord segment tangent

Properties of a circle are are as follows ;- Circumference, diameter, radius, tangent, sector, arc, chord and its segment

No. Assuming the measure of the arc is in some units of length along the curve, you have to divide the result by the circumference of the circle. Basically, you need to multiply the area of the whole circle by the fraction of the whole circle that the sector accounts for.

Circumference is the perimeter of a circle Diameter is the length spanning a circle cutting through its center Radius is half the length of a circle's diameter Tangent is a straight line that touches a circle's circumference at one point Arc is part of a circle's circumference Chord is a straight line joining any two points of a circle's circumference Sector is the area enclosed by an arc and two radii Segment is the area enclosed by arc and a chord Circle's circumference divided by its diameter is equal to the value of pi Area of a circle = pi*radius squared There are 360 degrees around a circle

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