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

Question

asked Mar 20, 2023 90.5k views

1 Answer

Rcreswick · Answer 1 · 2023-03-24T13:10:13+0000

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