Question

A center pivot irrigation system provides water to a sector shaped field, find the area of the field if 0=140 degrees and r= 40 yd

Answer 1

The area of the sector is approximately 1954.77 square yards.

A circular sector, also known as a circle sector or a disc sector (symbol:), is a piece of a disc (a closed region bordered by a circle) encompassed by two radii and an arc. The smaller area is known as the minor sector, and the bigger is known as the major sector.

Any point on the circle outside of the sector can be connected to the arc's endpoints to produce half of the central angle.

We know that the area of a circle is πr² and the area of the sector of a circle with angle θ is given by θ/360 πr² .

Area of the sector

= 140°/360°  × π × 40²

= 1954.7687... square yards.

≈ 1954.77 square yards.

Therefore the area of the sector is approximately 1452.113 square yards.

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