Answer:
[tex]r=16\text{ cm}[/tex]
Step-by-step explanation:
We have been given that in a circle a 45 degree sector has an area of [tex]32\pi\text{ cm}^2[/tex]. We are asked to find the radius of our given circle.
[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex]
Upon substituting our given values in above formula we will get,
[tex]32\pi\text{ cm}^2=\frac{45}{360}\times \pi r^2[/tex]
[tex]32\pi\text{ cm}^2=\frac{1}{8}\times \pi r^2[/tex]
Multiplying both sides of our equation by 8 we will get,
[tex]8\times 32\pi\text{ cm}^2=8\times\frac{1}{8}\times \pi r^2[/tex]
[tex]256\pi\text{ cm}^2=\pi r^2[/tex]
[tex]\frac{256\pi\text{ cm}^2}{\pi}=\frac{\pi r^2}{\pi}[/tex]
[tex]256\text{ cm}^2=r^2[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]\sqrt{256\text{ cm}^2}=r[/tex]
[tex]16\text{ cm}=r[/tex]
Therefore, the radius of our given circle is 16 cm.
