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# Calculate the circumference or area to solve each problem. Round to the nearest hundredth, if necessary.

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

Sep 5, 2017
edited by aschoenfeld  Sep 5, 2017

#1
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Alright, you'll have to excuse me if I get this question wrong. Not feeling very well today. 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
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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