Calculating Weight with Proportions for Balls of Different Sizes

[06Sport]

Proportion Help. (from Ratio, Proportion, and Variations)

Homework Statement

A ball 4.50 in in diameter weighs 18.0 oz. What is the weight of another ball of the same density that is 9.0 in in diameter?

Homework Equations

Is this set up as a proportion? Or something else? I read the similar figures things but that does not seem to work.

The Attempt at a Solution

I set it up like a proportion: 4.50/9 = 18/x this comes up with 36 oz. But this is not the right answer. The answer is supposed to be 144 oz. But they don't show how they got it. The book doesn't have anything like this in its examples so I am stuck.

Is this not set up like a proportion? Or is there another type of formula I should be using?

 

[Dick]

What's the relation between the volume of a sphere and its radius?

 

[HallsofIvy]

Yes, it is a proportion- but not just "volume is proportional to radius"- volume is proportional to a power of the radius: which power? As Dick said, "What is the relation between the volume of a sphere and its radius?"

 

[06Sport]

ok, so V= 4/3piD/2^3

then 18 = 4/3pi (4.5/2)^3
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2 = 4/3pi (4.5)^3 right?

cancellation gives me 18 / x = 1/8 / 1 which is 144 ! Great! thanks guys!