Answer:
1. (exact): 3π ft, (approx.): 9.4245 ft
2. (exact): 2.25π ft^2, (approx.): 7.068375 ft^2
Step-by-step explanation:
a) We are finding both the exact and approximate distance around the circular fire pit. This means we are finding the circumference of the circle. Let us start off with the equation for the circumference of the circle:
[tex]2\pi r[/tex]
We also know that the diameter of the circle is 3 ft. A radius is half a diameter, therefore, r = 1.5 ft. Let us now substitute this into the equation above:
[tex]2\pi *1.5=\\\\3\pi[/tex]
Therefore, the exact distance around the outside of the firepit is 3π ft.
Let us know find the approximate distance by substitute approximately 3.1415 into π. (π≈3.1415):
[tex]3\pi =\\3*3.1415=\\9.4245\\[/tex]
Therefore, the approximate distance around the outside of the firepit is 9.4245 ft. Please note that you may get a more accurate answer by substituting a π value with more digits.
b) We are now to find how much area the pit covers. This means we should find both the exact and approximate values of the area of the circle. Let us again start off with the equation of area for a circle:
[tex]\pi r^{2}[/tex]
Now let us substitute the radius, which we have found previously in part a into the equation:
[tex]\pi * 1.5^{2}=\\2.25\pi \\[/tex]
Therefore, the exact area around the outside of the firepit is 2.25π ft^2.
Let us know find the approximate area by substitute approximately 3.1415 into π. (π≈3.1415):
[tex]2.25\pi =\\2.25*3.1415=\\7.068375\\[/tex]
Therefore, the approximate area around the outside of the firepit is 7.068375 ft^2. Please note that you may get a more accurate answer by substituting a π value with more digits.
I hope this helps! Please let me know if you have any further questions :)
