Math

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Garden Area Problem. A designer created a garden
from two concentric circles whose equations are as follows:
(x+2)^2+(y-6)^2=16 and (x+2)^2+(y-6)^2=81
The area between the circles will be covered with grass. What is the area of that section?

How do you do this?

  • Math -

    The equation of a standard circle with centre at (a,b) and radius r is
    (x-a)² + (y-b)² = r²

    By inspection of the given circle,
    (x+2)^2+(y-6)^2=16 and (x+2)^2+(y-6)^2=81
    we conclude that both have centres at (-2,6), therefore they are concentric.

    The radii of the circles are √16=4 and √81=9.

    The area between the two circles are therefore
    πr1²-πr2²
    =π(9²-4²)
    =65π

  • Math -

    do you have any sites that explain this as well?

  • Math -

    The subject should be in any pre-calc textbook. Alternatively, you can google
    "equation of a circle".

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