Question

Suppose that circles A and B have a central angle measuring 40°. Additionally, circle A has a radius of

5/2 ft and the radius of circle B is
9 /2 ft.
If the measure of the sector for circle A is 25/36 π ft2, what is the measure of the sector for circle B?




















A)



2
9
π ft2


B)



4
9
π ft2


C)



9
4
π ft2


D)



9
2
π ft2

Answer 1

C.
`(9)/(4)\pi\text{ ft}^(2)`.

Explanation:

We have been given that circles A and B have a central angle measuring 40°. Additionally, circle A has a radius of 5/2 ft and the radius of circle B is 9 /2 ft.

Let us find measure of the sector of circle B using sector area formula.

`\text{Area of sector}=(1)/(2)*\frac{\text{Central angle}}{180}* \pi r^(2)`

Let us substitute our given values in sector area formula.

`\text{Area of sector of circle B}=(1)/(2)*(40)/(180)* \pi* ((9)/(2))^(2)`

`\text{Area of sector of circle B}=(40)/(360)* \pi* (81)/(4)`

`\text{Area of sector of circle B}=(1)/(9)* \pi* (81)/(4)`

`\text{Area of sector of circle B}=(9)/(4)\pi`

Therefore, the area of sector for circle B will be
`(9)/(4)\pi\text{ ft}^(2)` and option C is the correct choice.

Answer 2

The measure of the sector of circle B is given by:
A=θ/360πr²
But
θ=40°
r=9/2 ft
thus
A=40/360×π×(9/2)²
A=(9π)/4 ft²

Answer: C] (9π)/4 ft²