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Q: What is the area of a sector of a circle that has a diameter of ten inches if the length of the arc is ten inches?

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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.

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)

it's 25 sq in

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

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.

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

15 in

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

The sector area works out as: 10/10pi times 25pi = 25 square in.

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

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

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

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