Compute the exact length of arc AB.

Question

Answer 1

arc length = angle times radius (when angle is measured in radians; 90 = pi/2 radians)

length = (pi/2)8 = 4pi = about 4(3.14159) = 12. 57

or the length = 1/4 the circumference of a circle = (1/4)pid = (1/4)pi(2r) = (1/4)pi(2(8) = 4pi = about 12.57

Answer 2

Classic Geometry/ SAT question!

There are three ways to measure the attributes of a circle: area = pi*r^2; circumference = 2pi*r and degrees = 360. (radians as well, but that's just converted degrees)

The key for these problems is to understand a central angle (90 in our example) will create an angle (obviously<- read in snape voice) an arc and a wedge. These will all be proportional when compared to the whole circle. For example: The area of wedge/area of circle = length of arc / length of circle (aka circumference)

In this example, we are given the central angle = 90 degrees. 90 degrees /360 degrees = 1/4. This means the arc is also 1/4 the circumference.

Radius = 8 Circumference = 2*8 *pi = 16 pi Arc AB = 1/4* 16pi = 4pi

Hope this helps!

Answer 3

The length of the arc AB is one-fourth of the circumference.