Math CentralQuandaries & Queries


Question from Zach, a student:

A can of soda has a volume of 355 mL. The area of a circle is given as A=pieR2, where r= radius of the circle. So, the volume of the can is given by V=(pier2)h, where h is the height of the can. If a particular can has a height of 12.2 cm what is the radius of the can?

I know the answer is 3.04 cm. I need help figuring out how to arrive at this answer- what were the mathmatical steps?


Hi Zach.

Write down what you know. First here are the numbers we know:

V = 355
h = 12.2
π = about 3.14

Here is the formula we know:

V = πr²h

We can substitute in the numbers for the letters we know (I'm putting parentheses - brackets - around them so you can see what is happening):

[355] = [3.14] r² [12.2]

Now I have an equation (it has an equal sign, so it is an equation) with just one letter in it. So I want to isolate that on one side of the equal sign.

[3.14] r² [12.2] = 355

Divide by [3.14] and [12.2] on both sides so that those factors on the left cancel out and r² is left by itself:

r² = 355 ÷ [12.2] ÷3.14

r² = about 9.267

We want to know the radius r but we have r² instead. So we need to take the square root of both sides now:

√(r²) = √(9.267)

r = √(9.267)

r = about 3.04 cm

I hope this step by step explanation helps!
Stephen La Rocque.

PS: It is important for you to recognize in this question that 1 ml = 1 cm³. If the units were in fluid ounces and inches, you'd definitely have more work to do. Metric makes things quite simple.

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