Answer:
1. (<em>exact</em>): 3π ft, (<em>approx.</em>): 9.4245 ft
2. (<em>exact</em>): 2.25π ft^2, (<em>approx.</em>): 7.068375 ft^2
Step-by-step explanation:
a) We are finding both the <u>exact</u> and <u>approximate</u> distance around the circular fire pit. This means we are finding the <em>circumference</em><em> </em>of the circle. Let us start off with the equation for the circumference of the circle:
![2\pi r](https://tex.z-dn.net/?f=2%5Cpi%20r)
We also know that the <em>diameter</em> of the circle is 3 ft. A radius is half a diameter, therefore, <u>r = 1.5 ft.</u> Let us now substitute this into the equation above:
![2\pi *1.5=\\\\3\pi](https://tex.z-dn.net/?f=2%5Cpi%20%2A1.5%3D%5C%5C%5C%5C3%5Cpi)
Therefore, the <u>exact distance</u> around the outside of the firepit is 3π ft.
Let us know find the <u>approximate distance</u> by substitute approximately 3.1415 into π. (π≈3.1415):
![3\pi =\\3*3.1415=\\9.4245\\](https://tex.z-dn.net/?f=3%5Cpi%20%3D%5C%5C3%2A3.1415%3D%5C%5C9.4245%5C%5C)
Therefore, the <u>approximate distance</u> around the outside of the firepit is 9.4245 ft. <em>Please note that you may get a more accurate answer by substituting a π value with more digits. </em>
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b) We are now to find how much area the pit covers. This means we should find both the <u>exact</u> and <u>approximate</u> values of the area of the circle. Let us again start off with the equation of area for a circle:
![\pi r^{2}](https://tex.z-dn.net/?f=%5Cpi%20r%5E%7B2%7D)
Now let us substitute the radius, which we have found previously in <em>part a</em> into the equation:
![\pi * 1.5^{2}=\\2.25\pi \\](https://tex.z-dn.net/?f=%5Cpi%20%2A%201.5%5E%7B2%7D%3D%5C%5C2.25%5Cpi%20%5C%5C)
Therefore, the <u>exact area</u> around the outside of the firepit is 2.25π ft^2.
Let us know find the <u>approximate area</u> by substitute approximately 3.1415 into π. (π≈3.1415):
![2.25\pi =\\2.25*3.1415=\\7.068375\\](https://tex.z-dn.net/?f=2.25%5Cpi%20%3D%5C%5C2.25%2A3.1415%3D%5C%5C7.068375%5C%5C)
Therefore, the <u>approximate area</u> around the outside of the firepit is 7.068375 ft^2. <em>Please note that you may get a more accurate answer by substituting a π value with more digits. </em>
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<em>I hope this helps! Please let me know if you have any further questions :)</em>