Calculating Weight with Proportions for Balls of Different Sizes

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In summary, the problem involves finding the weight of a second ball with the same density as a given ball, but with a larger diameter. The solution is to set up a proportion using the volumes of the two balls, since volume is proportional to the cube of the radius. By correctly setting up the proportion, the answer is found to be 144 oz.
  • #1
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?
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  • #2
What's the relation between the volume of a sphere and its radius?
  • #3
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?"
  • #4
ok, so V= 4/3piD/2^3

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

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

What is "Proportion or No?"

"Proportion or No?" is a phrase commonly used in scientific research to describe a situation where the relationship between two variables is being investigated to determine if there is a proportional or non-proportional relationship between them.

How is proportionality determined?

Proportionality is typically determined by plotting the data on a graph and analyzing the shape of the resulting line or curve. A linear relationship indicates proportionality, while a non-linear relationship indicates non-proportionality.

What is the difference between proportional and non-proportional relationships?

In a proportional relationship, the ratio between the two variables remains constant regardless of the values of the variables. In a non-proportional relationship, the ratio between the variables changes as the values of the variables change.

How is proportionality important in scientific research?

Proportionality is important in scientific research because it helps to understand the relationship between two variables and make predictions based on this relationship. It also allows for the comparison of data and identification of patterns.

What are some examples of proportional and non-proportional relationships?

An example of a proportional relationship is the relationship between distance and time in which the speed remains constant. An example of a non-proportional relationship is the relationship between height and weight in which taller individuals may not necessarily weigh more than shorter individuals.

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