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What is the area of a sector of a circle with a radius of 8 inches and formed by a central angle that measures 60°?

a. 8π/3
b. 16π/3
c. 32π/3
d. 64π/3

User Sgupta
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1 Answer

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Final answer:

The area of the sector with a radius of 8 inches and a central angle of 60° is 32π/3 square inches. This is found by converting the central angle to radians and applying the sector area formula.

Step-by-step explanation:

The area of a sector of a circle can be found using the formula A = ½ r² θ, where A represents the area, r is the radius, and θ is the central angle in radians. Since there are 360 degrees in a full circle which corresponds to 2π radians, you can convert 60° to radians by multiplying by π / 180°. Therefore, the central angle in radians is (60°)(π / 180°) = π/3 radians.

Now we plug in the values into the area formula, we get A = ½ (8 in)² (π/3) which simplifies to A = 64π/6 in² or A = 32π/3 in². Therefore, the correct answer is c. 32π/3.

User Omkar Puttagunta
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