SOLUTION: 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 s
Algebra.Com
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?
=========================
The area at 3 inches is not relevant.
------------------
Using the area at r = 3 without using the formula,
RELATED QUESTIONS
The surface area of a sphere varies directly as the square of a radius.
a. if the... (answered by ewatrrr)
The surface area of a sphere varies directly as the square of the radius. If the surface... (answered by Alan3354)
the surface area of a sphere varies directly with the square of its radius. when the... (answered by addingup,advanced_Learner)
I have no idea what this is saying.
Solve the problem.
The surface area of a sphere... (answered by sudhanshu_kmr)
The surface area of a sphere varies directly with the square of its radius. If the... (answered by Alan3354)
The surface area of a ballon varies directly as the square of its radius. The Area is 325 (answered by mananth)
The surface of a balloon varies directly as the square of its radius. The area is {{{314... (answered by ankor@dixie-net.com)
The surface area of a sphere varies directly with the square of its radius. If the... (answered by scott8148,Earlsdon)
What is the radius of a sphere when its surface area is 113 square... (answered by Greenfinch)