Q: The area of a sector is the area of the circle multiplied by the fraction of the circle covered by that sector?

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That would certainly do it.

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)

If it is a sector of a circle then the arc is the curved part of the circle which forms a boundary of the sector.

It depends whether the UNSHOWN figure has the shaded sector as the sector which includes the 90° angle, or the one which excludes it. Assuming that it is the sector including the 90° angle, ie the question should have been written: What is the area of a sector of a circle with a radius of 3 units when the angle of the sector is 90°? It is a fraction of the whole area of the circle. The fraction is 90°/360° (as there are 360° in a full turn and only 90° are required) = 1/4 Area circle = π × radius² = π × (3 units)² = 9π square units → area 90° sector = ¼ × area circle = ¼ × 9π square units = 9π/4 square units ≈ 7.1 square units

There is no specific formula for a sector of a circle. There is a formula for its angle (at the centre), its perimeter, its area.

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That would certainly do it.

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)

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.

For A+ 7.22The area of a sector of a circle is proportional to the angle at the center of the sector, with 360 degrees corresponding to the full circle. Therefore, the area of the total circle for which the problem is stated is 50 X 360/110 = about 163.6 square units. The area of a circle is also equal to pi multiplied by the square of the radius of the circle, so that the radius r of this circle equals the square root of 163.6/pi = about 7.217 units. The circumference of the circle is also twice the radius multiplied by pi = 45 units, to the justified number of significant digits (limited by "50").a+ 45.33

Area of sector/Area of circle = Angle of sector/360o Area of sector = (Area of circle*Angle of sector)/360o

If it is a sector of a circle then the arc is the curved part of the circle which forms a boundary of the sector.

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

It depends whether the UNSHOWN figure has the shaded sector as the sector which includes the 90° angle, or the one which excludes it. Assuming that it is the sector including the 90° angle, ie the question should have been written: What is the area of a sector of a circle with a radius of 3 units when the angle of the sector is 90°? It is a fraction of the whole area of the circle. The fraction is 90°/360° (as there are 360° in a full turn and only 90° are required) = 1/4 Area circle = π × radius² = π × (3 units)² = 9π square units → area 90° sector = ¼ × area circle = ¼ × 9π square units = 9π/4 square units ≈ 7.1 square units

There is no specific formula for a sector of a circle. There is a formula for its angle (at the centre), its perimeter, its area.

It is a sector of the circle

The area of a whole circle is given by π x radius². The sector is a fraction of the whole circle which is the fraction of its angle of a full turn of 360° Thus area_sector = π x (38 m)² x 165°/360° = 3971/6 π m² ≈ 2079 m²