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