Lets get started :)
The First question:
Diameter = 20 ft
Radius = [tex] \frac{1}{2} [/tex] of 20 (diameter) = 20 ft
Area formula of a circle is
A = [tex] \pi [/tex]r²
=[tex] \pi [/tex](10)²
=100[tex] \pi [/tex] ft²
≈ 314 ft²
The answer will be the second option
The Second question:
radius of circle = 12mm divided into 20 sectors area
A = [tex] \pi [/tex]r²
= [tex] \pi [/tex](12)²
= 144[tex] \pi [/tex] ft²
Divide into 20 equal sector areas = [tex] \frac{144 \pi }{20} = 7.2 \pi [/tex]
≈ 22.6 mm²
Your answer will be the third option
The Third Question:
90°, sector area = 36[tex] \pi [/tex] , Radius = ?
[tex] \frac{angle}{360} = \frac{sector}{ \pi (r)^2} [/tex]
[tex] \frac{90}{360} = \frac{36 \pi }{ \pi r^2} [/tex]
[tex] \pi [/tex] and [tex] \pi [/tex] cancels out
We can now cross multiply
360 × 36 = 90r²
12960 = 90r²
Divide by 90 on either side
[tex] \frac{12960}{90} = \frac{90r^2}{90} [/tex]
144 = r²
Take squareroot
[tex] \sqrt{144} = x[/tex]
x = 12 in
Your answer will be the third option
