What is the area of the shaded segment in the following cases ?

Question

r=5cm,0=1/3 pi

0 meaning angle

Answer 1

The total area of a circle = pi r^2. If you wanted to know the total area of your circle with a radius = 5 cm you would square your radius and multiply that by pi. (5)^2 = 25 pi However, in this case, you are being asked to calculate the shaded (partial) region of a circle that is equal to 1/3 pi. The region under 1/3 pi is a 60 degree angle (coming off of the x axis and opening counterclockwise). This is just 1/6 of a complete circle, 60/360 = 1/6. To provide a mental picture, imagine a 90 degree angle (which would be equal to 1/2 pi). Obviously a 90 degree angle represents 1/4 of a complete circle, and you would divide the total area by 4. Back to your problem, the area under 1/3 pi is equal to 1/6 of the total area (which has already been calculated to be 25 pi) ...

Area = 1/6 of 25 pi = 25/6 pi

Hope that helps you! Good luck ...

Answer 2

Since the total angle in a circle is 2 pi, then the segment is

(1/3 pi) / 2 pi = 1/6 of total area of circle

Area = (1/6) * pi * r^2

Area = (1/6) * pi * 25

Area = 25 pi / 6

Answer 3

you r looking for the area of a sector i presume

area= angle/360 * pie*r^2=

60/360 * pie*0.05^2=.......work it out

note....1rad=180/pie degrees