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Question 935740: Suppose you are given a sphere with radius r. Which of the following quantities changes at a constant rate per unit change in r?
A. The circumference of the sphere divided by its volume
B. The volume of the sphere divided by its circumference
C. The area of the sphere divided by its volume
D. The volume of the sphere divided by its area
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! formula for circumference of the sphere = 4/3 * pi * r^3
formula for the area of the sphere is equal to 4 * pi * r^2
formula for the circumference of the sphere is equal to 2 * pi * r
circumference divided by volume is equal to (2 * pi * r) / (4/3 * pi * r^3) which simplifies to 3 / (2 * r^2).
the change is not constant per unit of r.
the volume of the sphere divided by its circumference is equal to (4/3 * pi * r^3) / (2 * pi * r) which simplifies to (2 * r^2) / 3.
the change is not constant per unit of r.
The area of the sphere divided by its volume is equal to (4 * pi * r^2) / (4/3 * pi * r^3) which simplifies to 3 / r.
the change is not constant per unit of r.
the volume of the sphere divided by its area is aequal to (4/3 * pi * r^3) / (4 * pi * r^2) which simplifies to r / 3.
this change is constant per unit change of r.
when r = 1, the ratio is 1/3.
when r = 2, the ratio is 2/3.
when r = 3, the ratio if 3/3.
when r = 4, the ratio is 4/3.
the ratio changes by 1/3 for every unit change in r.
selection D is your answer.
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