Question

In a circle a 45 degree sector has an area of 32 pie cm ^2 what is the radius of the circle

Answer 1

It is given that, 45/360 * πr² = 32π
1/8 * πr² = 32π
πr² = 256π
r² = 256
r = √256
r = 16

In short, Radius of the Circle would be 16 cm

Hope this helps!

Answer 2

`r=16\text{ cm}`

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}=(\theta)/(360)* \pi r^2`

Upon substituting our given values in above formula we will get,

`32\pi\text{ cm}^2=(45)/(360)* \pi r^2`

`32\pi\text{ cm}^2=(1)/(8)* \pi r^2`

Multiplying both sides of our equation by 8 we will get,

`8* 32\pi\text{ cm}^2=8*(1)/(8)* \pi r^2`

`256\pi\text{ cm}^2=\pi r^2`

`\frac{256\pi\text{ cm}^2}{\pi}=(\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.