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What is the area of a sector with radius 6" and measure of arc equal to 120°?

Answer 1

Claire Akin

Arc length #color(red)(s = 12.5664”)#

Circumference #c = 2 pi r#

Arc length #s = (theta^0 / 360^0 )(2 pi r) #

#s = (120 / 360) * 2pi * 6 = 4 pi = color (red)(12.5664”)#

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Answer 2

Savannah Aguilar

To find the area of a sector with a radius of 6 inches and a measure of arc equal to 120°, you can use the formula for the area of a sector, which is (θ/360) * π * r^2, where θ is the measure of the central angle in degrees, π is pi (approximately 3.14159), and r is the radius of the sector.

Substitute the given values into the formula:

θ = 120° r = 6 inches

Calculate the area using the formula:

Area = (120/360) * π * (6)^2

Simplify the expression:

Area = (1/3) * π * 36

Area = 12 * π

Using an approximation for π, such as 3.14159, calculate the final result:

Area ≈ 12 * 3.14159

Area ≈ 37.6991 square inches

Therefore, the area of the sector is approximately 37.6991 square inches.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.