Question 1107158: Hello Online tutors!
Here's my question:
The surface area of a sphere is A=4pir^2(If you didn't get that it was 4 times pi times r to the second power. All one expression.
Rest of the question:
If the area of a circle is the same as the surface area of a sphere, find the ratio of the radius of the sphere to the radius of the circle.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the area of a circle is equal to pi * r^2.
the surface area of a sphere is equal to 4 * pi * r^2.
assume the radius of the circle is x.
assume the radius of the sphere is y.
the area of the circle becomes pi * x^2
the surface area of the sphere becomes 4 * pi * y^2
let A be the surface area of the sphere.
since they're the same, let A also be the area of the circle.
you get A = pi * x^2 and A = 4 * pi * x^2
since the areas are the same, you get pi * x^2 = 4 * pi * y^2
divide both sides of this equation by pi and you get x^2 = 4 * y^2
divide both sides of this equation by y^2 and you get x^2 / y^2 = 4
take the square root of both sides of this equation and you get x/y = 2
solve for x to get x = 2y.
solve for y to get y = 1/2 * x.
x is the radius of the circle.
y is the radius of the sphere.
if the radius of the circle is 2 times the radius of the sphere, then the area of the circle will be the same as the surface area of the sphere.
if the radius of the sphere is 1/2 times the radius of the circle, then the surface area of the sphere will be the same as the area of the circle.
let's see if this is correct.
assume the radius of the circle is 8 and the radius of the sphere is 4.
the ratio of the radius of the circle to the radius of the sphere is 8/4 = 2.
the ratio of the radius of the sphere to the radius of the circle is 4/8 = 1/2.
the area of the circle is equal to pi * 8^2 which is equal to 64 * pi.
the surface area of the sphere is equal to 4 * pi * 4^2 which is equal to 4 * pi * 16 which is equal to 64 * pi.
the areas are the same which confirms that the solution is correct.
the solution is that the ratio of the radius of the sphere to the radius of the circle is 1/2.
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