Question

PLEASE ANSWER ASAP DONT BE A SCAME

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 explanation that justifies how the area of a sector of a circle is derived is 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.

To find the area of a sector of a circle, first, determine the fraction of the circle that the sector represents. This can be done by dividing the central angle of the sector by the total number of degrees in a circle (which is 360 degrees). This will give you the fraction of the circle that the sector represents.

Next, multiply this fraction by the area of the entire circle. The area of a circle can be calculated using the formula A = πr^2, where A is the area, r is the radius of the circle, and π is a constant equal to approximately 3.14.

So, the formula for finding the area of a sector of a circle is:

Area of sector = (central angle/360) x πr^2

This formula allows you to calculate the area of any sector of a circle, regardless of the size of the circle or the size of the sector.