Question

http://assets.openstudy.com/updates/attachments/501bd8c1e4b02742c0b2e1b5-ayeeraee-1344004715914-35.jpg
Will someone help me answer these questions about this picture.
How much area will each delivery radius cover?
Write the equation for each circle created.
Please show your work for all calculations.

Answer 1

area of a circle is => \(\bf \large \pi r^2\)
r = radius

as far as the equation of those circles shaded there, well, look at their center point, is the origin, and now look at their respective \(\bf \text{radius}\)
now use the circle equation => http://www.mathwarehouse.com/geometry/circle/images/equation-of-circle/general-formula-equation-of-circle.png

Answer 2

I still don't understand how to solve the equation, can you set it up for me?

Answer 3

well, let's take the smaller circle, what's the center of it?
and what's it's radius?

Answer 4

well its radius is 4

Answer 5

center is (0,0)

Answer 6

center = (h, k), radius "r"
\(\bf (x-h)^2+(y-k)^2 = r^2
(x-(0))^2+(y-(0))^2 = (4)^2\\ \large \implies x^2+y^2=16\)

Answer 7

so that would be the delivery radius of the small circle?

Answer 8

yes

Answer 9

and you do the same for the other
whose radius is 7 and the center is the origin too

Answer 10

ok I will try one minute

Answer 11

so it would be 49?

Answer 12

yes
\(\bf (x-h)^2+(y-k)^2 = r^2\\
(x-(0))^2+(y-(0))^2 = (7)^2 \implies \color{blue}{ x^2+y^2=49}\)

Answer 13

so does that answer all of the questions it asks?

Answer 14

why does it say write the equation for each circle created

Answer 15

yes, just get the Area of each circle using the area equation of \(\bf \large \pi r^2\)

Answer 16

so the small circle would have an area of 50.24?

Answer 17

and the large circle would have an area of 153.86?

Answer 18

yes

Answer 19

\(50.24\ miles^2\) square whatever unit is used, kilometers, yards, else :)

Answer 20

okay thank you so much

Answer 21

yw