find the area of the sector of a circle whose radius is 5cm and has a central angle of 120degrees.?
- MaverickLv 71 decade agoFavorite Answer
In general, to do area of sector problems, you want to find the total area of the circle and then find only the area of that portion of the circle you are looking for. For example, in your case, the area of the circle can be found by the formula A = pi*r^2. Now, what you are looking for is only the portion which covers the central angle of 120 degrees. An entire circle is 360 degrees, so the area that you want is 120/360 of the entire circle. (note: this reduces to 1/3!
so, it is 1/3*pi*r^2
A general formula is:
x/360*pi*r^2; where x is the measure of the central angle of the portion that you are looking for.
Also, you probably will have problems that ask for the length of the arc formed by a central angle. The principle for finding these is the same, except you multiply the portion of the entire circle by the circumference.
Arc Length = x/360*pi*d ; where x is the measure of the central angle and pi*d is the circumference.
Both are good formulas to memorize
Good Luck - M
- Anonymous1 decade ago
The area of a circle = pi * radius squared
you dont have a whole circle, you have 120/360 of a circle.
so multiply the area of your circle by the ration above
area= 120/360 * 3.14159 * 5 x 5 = 26.18 sq cm.
- TwiggyLv 71 decade ago
The area = 120/360 x pi r^2
= 1/3 x 3.142 x 5 x 5....
I`m sure you can work it out.
Hope I`ve helped, Twiggy.
- corneliusLv 44 years ago
radius - r arc length = 24 cm = (r) x (theta) = 24cm ................(a million) element of asector = (theta /2pi ) x pi x r^2 = a million/2 x theta x r^2 = 180cm^2 .................(2) fixing, we get r/2 = 15/2 cm r = 15cm theta= 24/15 = 8/5 = a million.6 radians