Home > Geometry > Circumference and Area of Circles

A chord with a length of #18 # runs from #pi/12 # to #pi/2 # radians on a circle. What is the area of the circle?

Answer 1

Mason Adams

Area of the circle is 685.6567

Chord length = 18
#theta = (pi/2) - (pi/12) = (5pi) / 12#
#R = (c/2) / sin (theta/2) = (18/2)/sin ((5pi)/24) = 14.7841#

Area of the circle = #pi R^2 = pi* 14.7841^2 = 685.6567#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

James Atkins

The length of a chord in a circle can be related to the radius of the circle and the central angle subtended by the chord. Using the formula for the length of a chord given by ( L = 2r\sin\left(\frac{\theta}{2}\right) ), where ( L ) is the length of the chord, ( r ) is the radius of the circle, and ( \theta ) is the central angle in radians, we can solve for the radius of the circle. Once we have the radius, we can use the formula for the area of a circle, ( A = \pi r^2 ), to find the area of the circle.

By signing up, you agree to our Terms of Service and Privacy Policy

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.