SOLUTION: I need a little help with this one please. Find a polynomial for the sum of the areas of three circles. The first circle has an unknown radius, the second one has a radius of 3, an

Question 244876: I need a little help with this one please. Find a polynomial for the sum of the areas of three circles. The first circle has an unknown radius, the second one has a radius of 3, and the third a radius of 2. Help is greatly appreciated.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
area of a circle is equal to pi * r^2 where pi is equal to is equal to 3.141592654 and r is the radius of the circle.

let A[i] = the area of circle i.

[] means sub as in A[i] means A sub i.

i can be 1, 2, or 3.

let S = A[1] + A[2] + A[3]

A[1] = pi * r[1]^2 because the radius is not known.

A[2] = pi * 3^2 because the radius is 3.

A[3] = pi * 2^2 because the radius is 2.

You get:

S = pi*r[1]^2 + pi*3^2 + pi*2^2

This becomes:

S = pi*r[1]^2 + pi*9 + pi*4

factor out the pi to get:

S = pi * (r[1]^2 + 9 + 4)

combine like terms to get:

S = pi * (r[1]^2 + 13)

I think that's your polynomial in its simplest form.

to solve for r[1], you would need to know S.

to solve for S, you would need to know r[1].

S is the sum of all three areas.

r[1] is the radius for the first circle.

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