Question

A circle is shown below.What is the area of the unshaded sector?A. 2pi square unitsB. 8pi square unitsC. 56pi square unitsD. 48pi square units

Answer 1

we know that

The area of complete circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of the sector with a central angle of 45 degrees

`(pi\cdot r^2)/(360)=(x)/(45)`

we have

r=8 units

substitute and solve for x

`\begin{gathered} (pi\cdot(8)^2)/(360)=(x)/(45) \\ \\ x=\pi\cdot64\cdot(45)/(360) \\ x=8\pi\text{ units\textasciicircum{}2} \end{gathered}`

therefore

the answer is 8pi square units

option B