Question

PLEASE ANSWER ASAP

Which explanation justifies how the area of a sector of a circle is derived?

A. The sector of a circle is a fractional part of the circle. Determine the fraction of the
circle that the sector represents. Multiply this fraction by the area of the entire circle.

B. Determine the percent of the sector of the circle divided by the degrees in a circle. Then find the number of triangles within a circle. Divide the two numbers and multiply by the area of the circle.


C. Find how many sector pieces fit in a circle. Divide this number by the total degrees in a circle. Then multiply the quotient by the diameter of the circle.

D. The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle.

Answer 1

The correct explanation is **A.**

The area of a sector of a circle is derived by determining the fraction of the circle that the sector represents. This fraction is then multiplied by the area of the entire circle.

For example, if a sector of a circle has an angle of 60 degrees, then it represents 1/6 of the circle. The area of the sector is then calculated as follows:

```

Area of sector = (1/6) * Area of circle

```

```

Area of sector = (1/6) * πr²

```

```

Area of sector = (πr²) / 6

```

The other explanations are incorrect.

* Explanation B is incorrect because the number of triangles within a circle is not relevant to the area of a sector.

* Explanation C is incorrect because the number of sector pieces that fit in a circle does not determine the area of a sector.

* Explanation D is incorrect because the number of sections of the sectors that fit in the circle does not determine the area of a sector.

Explanation: