SOLUTION: Hello! What is the radius of a sphere whose area is equal to the sum of the areas of four circles of radius 7?

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Question 1133040: Hello!
What is the radius of a sphere whose area is equal to the sum of the areas of four circles of radius 7?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Area of 4 circles of radius 7 is 4*pi*7^2 or 4*49 pi or 196 pi
A of sphere is therefore 196 pi
that equals 4pi*r^2
pi s cancel
4r^2=196
r^2=49
r=7 of sphere

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The area of a circle is %28pi%29%28r%5E2%29.

The area of 4 circles each with the same radius is 4%28pi%29%28r%5E2%29.

The surface area of a sphere is %284pi%29%28r%5E2%29.

Those last two area formulas are identical; the surface area of a sphere with radius r is equal to the areas of 4 circles with radius r.

Since in this problem the circles have radius 7, the sphere also has radius 7.