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?

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) (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) (Show Source): You can put this solution on YOUR website!

The area of a circle is .

The area of 4 circles each with the same radius is .

The surface area of a sphere is .

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.
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