



 
Hi Gilligan. When we ask you to "express a certain variable as a function of another variable" we mean to construct a function such that you can feed one variable into it and get the other variable.
What I wrote above is expressing y as a function of x. I could say, "Change that to express x as a function of y" and you would transform it into the equivalent equation:
So "express the volume V as a function of r" means get V by itself on the left side of the equal sign and r (and no other variables) in an expression on the right side of the equal sign. Here's another example. The Area of a circle is A = πr². The Circumference of a circle is C = 2πr. Express the Area A as a function of the Circumference C. This means provide an equation with just A in it and C in it, where A is the only thing on the left hand side and there are no variables other than C on the right side. Here's how I'd solve this: C = 2πr, therefore r = C / (2π). Substitute this into A = πr² and I have A = π[ C / (2π) ]². This simplifies to A = C² / (4π). That's the answer. Now you should be able to tackle your question.  


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