Question 1187680: The surface area of a sphere varies directly as the square of the radius. If the surface
area is 36𝜋 𝑖𝑛
2 when the radius is 3 inches, what is the surface area of the sphere with
a radius of 5 inches?
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the direct variation formula is y = k * x
when x = r^2, the formula becomes y = k * r^2.
when r = 3 and y = 36 * pi, the formula becomes 36 * pi = k * 3^2
simplify to get 36 * pi = k * 9
solve for k to get k = 36 * pi / 9 = 4 * pi.
now that you have the value of k, you can solve for y when r = 5.
the formula of y = k * r^2 becomes y = 4 * pi * 5^2 which becomes y = 4 * pi * 25 which becomes y = 100 * pi.
k, being the constant of variation, doesn't change, as long as you're dealint with the surface area of a sphere.
if you look up the formula for the surface area of a sphere, you will find that the formula is y = 4 * pi * r^2, where y is the surface area of the sphere.
4 * pi remains the same, regardless of the measure of the radius.
it becomes the constant of variation in that formula.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! The surface area of a sphere varies directly as the square of the radius. If the surface
area is 36𝜋 𝑖𝑛
2 when the radius is 3 inches, what is the surface area of the sphere with
a radius of 5 inches?
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The area at 3 inches is not relevant.
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Using the area at r = 3 without using the formula, 
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