Answer :
Part 1: Circumference of circle = [tex]105.20[/tex] inches & Area of circle = [tex]880.97 inches^{2}[/tex]
Part 2: Area of circle = [tex]3.14 ft^{2}[/tex]
Part 3: Area of square not covered by circle = [tex]29.69inches^{2}[/tex].
Step-by-step explanation:
Part 1:
We have radius of circle as [tex]16\frac{3}{4} = 16.75 inches[/tex] . Let's find area & circumference of circle:
Circumference of circle = [tex]2\pi r[/tex]
⇒ Circumference of circle = [tex]2\pi r[/tex]
⇒ Circumference of circle = [tex]2\pi r[/tex] = [tex]2(3.14)(16.75)[/tex]
⇒ Circumference of circle = [tex]105.20[/tex] inches
Area of circle = [tex]\pi r^{2}[/tex]
⇒ Area of circle= [tex]\pi r^{2}[/tex]
⇒Area of circle = [tex]\pi r^{2}[/tex] = [tex](3.14)(16.75)^{2}[/tex]
⇒ Area of circle = [tex]880.97 inches^{2}[/tex]
Part 2:
Circumference of circle = [tex]2\pi r[/tex] = [tex]6.28ft[/tex]
⇒ [tex]2\pi r = 6.28[/tex]
⇒ [tex]r = \frac{6.28}{2\pi } = \frac{6.28}{2(3.14)} = 1 ft[/tex]
Area of circle = [tex]\pi r^{2}[/tex]
⇒Area of circle = [tex]\pi r^{2}[/tex] = [tex](3.14)(1)^{2}[/tex]
⇒ Area of circle = [tex]3.14 ft^{2}[/tex]
Part 3:
Perimeter of square = [tex]4a[/tex] , a is side of square.
⇒ [tex]4a = 47[/tex]
⇒ [tex]a = \frac{47}{4}[/tex]
⇒ a = [tex]11.75 inch[/tex]
Since radius of circle inscribed in square is half of side of square i.e.
[tex]radius = \frac{a}{2}\\ radius = r = \frac{11.75}{2}[/tex]
[tex]r = 5.875inch[/tex]
Now, Area of square not covered by circle = Area of square - area of circle
⇒ [tex]a^{2} - \pi r^{2}[/tex]
⇒ [tex]11.75^{2} - 3.14(5.875)^{2}[/tex]
⇒ [tex]29.69inches^{2}[/tex]
∴ Area of square not covered by circle = [tex]29.69inches^{2}[/tex].
