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A chord with a length of #8 # runs from #pi/12 # to #pi/8 # radians on a circle. What is the area of the circle?

Answer 1

Autumn Armstrong

Area of the circle is 11,750.9632

Chord length = 8
#theta = (pi/8) - (pi/12) = (pi) / 24#
#R = (c/2) / sin (theta/2) = (8/2)/sin ((pi)/48) = 61.1592#

Area of the circle = #pi R^2 = pi* 61.1592^2 = 11,750.9632#

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Answer 2

Parker Allen

To find the area of the circle, you can use the formula for the area of a sector. First, you need to find the radius of the circle using the given chord length and the angle subtended by the chord.

The formula to find the radius (r) using the chord length (c) and the angle (θ) in radians is:

[ r = \frac{c}{2 \times \sin\left(\frac{\theta}{2}\right)} ]

Given that the chord length (c) is 8 units and the angle (θ) is (\frac{\pi}{8} - \frac{\pi}{12} = \frac{\pi}{24}) radians, you can calculate the radius using the formula.

Then, once you have the radius, you can use the formula for the area of a circle:

[ A = \pi r^2 ]

Substitute the calculated radius into this formula to find the area of the circle.

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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.