Area if Sector

[dim hemlock]

The diameter of a circle is 8 feet. What is the angle measure of an arc bounding a sector with area 6​𝜋 square feet?

[azure parrot]

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[dim hemlock]

r=4 which then goes to 16

is it 16/360 times 6pi?

[sacred wagon]

The area of a sector is a percentage of the area of the circle, right?

[hearty verge]

360×the proportion of the arc that the purple is, divided by the total circumference

or the area proportion here

360×6π/16π
135°

[dim hemlock]

ok ok

[hearty verge]

like how you represent a pie chart

[dim hemlock]

can i divide 360 by 16 then multiply by 6pi too?

i understand im js wondering if i can do that too

[hearty verge]

well you divide 360 by 16π

πr² for area

and then you can multiply by 6π

[buoyant heart]

Area of sector = 6π
theta/360° × πr² = 6π
theta = 6π/π(4)² × 360°

theta = 135°

[dim hemlock]

huhhhh

16/6pi times 360 basically?>

The radius of a circle is 10 centimeters. What is the angle measure of an arc bounding a sector with area 15​𝜋 square centimeters?

im stuck on this one too

r goes to 100

so do i do 100/360 x15pi?

[hearty verge]

it's 15π/100π × 360

you have the find the proportion of areas

and multiply it by the total angle

[dim hemlock]

i got 54

can i use this for any prob?

The diameter of a circle is 16 feet. What is the angle measure of an arc bounding a sector with area 12​𝜋 square feet?

like this cause i got a decimal

[hearty verge]

8²=64
12π/64π × 360

67.5°