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The distance around the edge of a pool is 38 feet. Find the area that the pool will cover.

ASAP PLEASE

 Sep 5, 2017
edited by aschoenfeld  Sep 5, 2017
 #1
avatar+558 
+1

Alright, you'll have to excuse me if I get this question wrong. Not feeling very well today. laugh

 

The distance around the pool would be the circumference.

Considering the pool is a circle.

 

The formula to get the circumference of a circle is 2*pi*r.

 

So, we have the equation 2*pi*r = 38.

Divide both sides by 2 to get pi*r = 19.

Divide both sides by pi to get r = 19/pi. Put that in a calculator and get r = 6.0478878374920228...

Don't round it yet. Well, you could, but you would get a less accurate answer.

 

The formula to get the area of a circle is pi*r^2. 

So we plug in r (which is 6.0478878374920228) into this equation.

pi*(6.0478878374920228)^2

Just plug that all into a calculator and get 114.9098689123484339749.

Round that to the nearest hundredth and get 114.91 feet^2  (Because it's the area)

114.91 feet^2.

 Sep 5, 2017
 #2
avatar+2340 
+1

Yes, assuming it is a circle (which I believe it is because "circumference" is used in the title), the area is indeed 0\(114.91ft^2\). Apparently, being ill does not obstruct your computational abilities. I hope you get better soon!

 

Of course, \(r=\frac{19}{\pi}\), and the area of a circle is \(\pi r^2\). Plugging what we know for r, we ge tthe following:

 

\(\pi*\left(\frac{19}{\pi}\right)^2\) Distribute the exponent to both the numerator and denominator.
\(\left(\frac{19}{\pi}\right)^2=\frac{19^2}{\pi^2}=\frac{361}{\pi^2}\)  
\(\frac{\pi}{1}*\frac{361}{\pi^2}\) Before multiplying the fractions together, notice that there is a common factor of pi in both the numerator of one fraction anf the denominator in another.
\(\frac{361}{\pi}\approx114.91ft^2\)  
   

 

In other words, good job!

TheXSquaredFactor  Sep 5, 2017

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