A circle has a sector with area 27\pi27π27, pi and central angle of \purple{120^\circ}120 ∘ start color #9d38bd, 120, degrees, e nd color #9d38bd. What is the area of the circle?
2 answers:
Answer:
The radius of the circle is 9 units.
Step-by-step explanation:
To calculate the area of the circle we need to find it's radius, since we have the area of the sector and it's angle, therefore we can calculate the radius by using the following formula:
sector area = (central angle)*pi*r²/360
27pi = 120*pi*r²/360
27pi = pi*r²/3
27 = r²/3
r² = 81
r = sqrt(81) = 9
The radius of the circle is 9 units.
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