The equation for the area of the circumference sectors is given by:
[tex] A = (\frac{S'}{S}) * \pi * r ^ 2
[/tex]
Where,
S ': is the central angle
S: it is the complete angle of the cirfunference
r: is the radius of the circumference
On the other hand, we must bear in mind that the area of a circle is:
[tex] Ac = \pi * r ^ 2
[/tex]
Therefore, the area of the sector can be rewritten as:
[tex] A = (\frac{S'}{S}) * Ac
[/tex]
Answer:
According to the definition, the following statements are true:
1) The area of a circle depends on the length of the radius.
2) The area of the sector depends on the ratio of the central angle to the entire circle.
3) The area of a sector depends on pi.
4) The area of the entire circle can be used to find the area of the sector.
Options (1) and (2) are the correct options.
We need to check the given statements that apply for the area of circles and sectors:
(1) The area of a circle depends on the length of the radius.
Yes, the above statement is true. The area of the circle can only be dependent on the length of the radius.
(2) The area of a sector depends on the ratio of the central angle to the entire circle.
Yes, the above statement is also true. The area of a sector depends on the ratio of the central angle to the entire circle.
(3) The area of a sector depends on a [tex]\pi[/tex].
No, it is a constant and always gives a definite value.
(4) The area of the entire circle can be used to find the area of a sector.
No, you can use the fraction of the area of the entire circle to find the area of a sector.
(5) The area of a sector can be used to find the area of a circle.
No, the area of a sector can not be used to find the area of a circle.
Thus, options (1) and (2) are the correct options.
To know more about the area of circles, please refer to the link:
https://brainly.com/question/20767796
