Question 1159148
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For each case, find the area of the whole circle with the given radius.  Then use the given central angle to find the fraction of a circle it represents.  Multiply the whole area by that fraction to find the area of the sector.<br>
A. central angle 135 degrees; radius 2 square root 2
The area of the whole circle is {{{(pi)(2sqrt(2))^2 = 8pi}}}
135 degrees us 135/360 = 3/8 of the whole circle
area: {{{(3/8)*8pi = 3pi}}}<br>
B. central angle 80 degrees; radius 3
The area of the whole circle is {{{(pi)(3)^2 = 9pi}}}
80 degrees us 80/360 = 2/9 of the whole circle
area: {{{(2/9)*9pi = 2pi}}}<br>
C. central angle 67.5 degrees; radius 4
The area of the whole circle is {{{(pi)(4)^2 = 16pi}}}
67.5 degrees us 67.5/360 = 3/16 of the whole circle
area: {{{(3/16)*16pi = 3pi}}}<br>
D. central angle 270 degrees; diameter 4
The area of the whole circle is {{{(pi)(2)^2 = 4pi}}}
270 degrees us 270/360 = 3/4 of the whole circle
area: {{{(3/4)*4pi = 3pi}}}<br>