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A chord with a length of #1 # runs from #pi/12 # to #pi/2 # radians on a circle. What is the area of the circle?

Answer 1

Ella Armstrong

Area of the circle #A_c =color(green)(~~ 28.2743# sq units

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Answer 2

Theodore Abad

The area of the circle can be calculated using the formula:

[ A = \pi r^2 ]

where ( r ) is the radius of the circle.

To find the radius, first calculate the length of the arc that corresponds to the given chord using the formula:

[ \text{Arc Length} = r \times \text{central angle in radians} ]

Given that the chord length is 1 and the central angle is ( \frac{\pi}{2} - \frac{\pi}{12} = \frac{5\pi}{12} ), we can find the radius.

Then, plug the radius into the formula for the area of the circle to find the area.

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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.