Question

Which statements are true regarding the area of circles and sectors? Check all that apply.
The area of a circle depends on the length of the radius.
The area of a sector depends on the ratio of the central angle to the entire circle.
The area of a sector depends on pi.
The area of the entire circle can be used to find the area of a sector.
The area of a sector can be used to find the area of a circle.

Answer 1

\[A_{circle} = \pi*r^{2}\]

Answer 2

so its the first one?

Answer 3

based on that formula does the area of the circle depend on the length of the radius?

Answer 4

noo

Answer 5

i dont know

Answer 6

look at the formula

Answer 7

it will make sense, let me show you

say if the radius is 4

and we double it to 8

Answer 8

okay

Answer 9

\[\pi*(4)^{2} = 16\pi\]

\[\pi*(8)^{2} = 64\pi\]

take a look at the two radii 4 and 8 look what happens to the area? can you tell me how radius affects area?

Answer 10

the area increases

Answer 11

yep and why?

Answer 12

because the radi increases

Answer 13

exactly so what can we say about A

Answer 14

for an area of a sector where theta is the angle made by the sector

\[\frac{ \theta }{ 360 }*\pi*r^{2}\]

Answer 15

well the area of a sector depends on pi it also depends on r too.

Answer 16

pi*r^2 is the area of the entire circle so yeah it can be used to find the area of a sector, same with the area of the sector.