SOLUTION: The volume of a cone varies jointly as its height and the square of its radius. If
the volume of a cone is 32π cubic inches when the radius is 4 inches and the height is 6 in
Algebra.Com
Question 1127601: The volume of a cone varies jointly as its height and the square of its radius. If
the volume of a cone is 32π cubic inches when the radius is 4 inches and the height is 6 inches,
find the volume of a cone when the radius is 4 inches and the height is 10 inches.
I got this question wrong on the homework, and need to understand the proper steps. Could you please break it down for me? Thank you!
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
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The volume of a cone varies jointly as its height and the square of its radius.
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v, volume
h, height
r, radius
k, variation constant
The description translated is .
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If
the volume of a cone is 32π cubic inches when the radius is 4 inches and the height is 6 inches,...
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you can find k, through substituting those given values.
.
.
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
In the answer from the other tutor, they started on the problem by finding the constant of variation, using the given information.
But then they didn't answer the question....
That would have been a valid approach to solving the problem. And it would have been an appropriate method if you need to get a complete formula for the volume, including the constant of variation -- for example, if you needed a formula to use for finding the volume of several cones.
But, in this problem, you only need to find the volume of one other cone. The easiest way to do that is by looking at how each variable changes.
The problem says the volume varies jointly as the height and the square of the radius.
From the first cone to the second, the radius doesn't change at all, so the only change in the volume will be due to the change in height.
From the first cone to the second, the height changes from 6 to 10, and increase by a factor of 10/6 = 5/3.
So the volume will increase by that same factor.
The volume of the second cone is 160/3 pi.
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