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Algebra Blues


Summer is over. Which brings us to the question we’ve all been contemplating over the last few months:

What is the radius (r) of a sphere the surface area (sa) of which is 46π cm2?

First, we write out the equation.
Teaching this, I find it helpful to color-code the factors to make it easier to follow them when we invert the equation to find the radius.
Since the sa of a sphere = 4πr2, we write the equation thus:

sa = r2 = 46π cm2

Then we invert the equation to find the radius:

r = 46π cm2
       

Eliminate the factors common to numerator and denominator:

r = √46π cm2
       4π

r = √46 cm2
       4 2   (4 = 22)

And the solution is:

r = √46/2 cm*

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School is in session. The problem above is easy, just a review from Algebra 1, but I’ve got a whole year of teaching Algebra 2 ahead of me. Math is fun, and that’s no joke. I really do enjoy it. But teaching it is somewhat less fun at times. Buy stock in McNeil-PPC.

* Solution corrected thanks to Aric.



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7 Comments:


#1 || 09·09·18··09:09 || Kim in ON

Oh, I well remember teaching that to my daughter when we homeschooled her... I could only manage Algebra 1... the math expert had to take over with Algebra 2.


#2 || 09·09·18··09:11 || Aric

Not to be overly picky, but shouldn't the 2 be outside the sq rt symbol? I can't make the symbol in the comments, but the radius would be sq rt (46) divided by 2 cm. It looks like you have the radius as sq rt of (46/2).


#3 || 09·09·18··09:29 || David

Well, Aric, this is math, so it’s either right or wrong. You can’t be too picky.

My solution is correct. The confusion (I think) is that the whole expression

46π cm²
   4π

should have been inside the radical (√) to begin with. I couldn't do that with text. I probably should have written it like so:

46π cm² /4π


#4 || 09·09·18··09:39 || Aric

I know it's been a while since I had to teach it, but when you have the 46/4 in the radical (read: rt(46/4), it is the same as rt(46)/rt(4), which leaves the answer as rt(46)/2.

So, the solution should be rt(46)/2, not rt(46/2) {since the sq rt of 4 is 2, not still rt(2), the 2 is not included under the radical}

Boy, this would be easier if I could make a sq rt sign!


#5 || 09·09·18··10:00 || David

You can type the relevant symbols like so:
√ = √
² = ²

I still think I’m right, but I’m going to consult the book before arguing further. Just so I don’t multiply my embarrassment exponentially.


#6 || 09·09·18··10:10 || David

Aric,
   You are indeed correct. I goofed. Thanks for the correction.


#7 || 09·09·18··10:15 || Aric

Glad I could help. Best of luck with your Alg 2.


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