SOLUTION: The ratio of the length of arc of a circle to the circumference of the circle is 3:7, If the diameter of the circle is 14 cm, Calculate, correct to three significant figures (a) p

Algebra ->  Test -> SOLUTION: The ratio of the length of arc of a circle to the circumference of the circle is 3:7, If the diameter of the circle is 14 cm, Calculate, correct to three significant figures (a) p      Log On


   

Question 1151931: The ratio of the length of arc of a circle to the circumference of the circle is 3:7, If the diameter of the circle is 14 cm, Calculate, correct to three significant figures
(a) perimeter of the minor sector
(b) area of the minor sector
Take pi = 22/7
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of the length of arc of a circle to the circumference+of the circle is 3%3A7:

arc%2Fc=3%2F7
since c=d%2Api and the diameter of the circle is d=14+
c=14%2A%28+22%2F7%29
c=2%2A22
c=44
now we can find the length of arc
arc%2F44=3%2F7
arc=%283%2F7%2944
arc=18.857=> the length of the arc; let it be arc=L

(a) perimeter of the minor sector
the perimeter P of the sector is L%2B2r units
P=18.857%2B2%2A7
P=32.857




(b) area of the minor sector
The area of a sector of a circle is A=%281%2F2%29+r%5E2%2A+theta, where r is the radius and theta the angle in radians subtended by the arc at the center of the circle.
‭first, we need to find the angle theta in radians
18.857%2F32.857+=%28theta+%2F+360+%29
+theta=%28+18.857%2F32.857%29+360+%29

theta+=0.5739%2A360
theta+=++206.604° => theta+=3.6059 radians

A=%281%2F2%29+r%5E2%2A+theta
A=%281%2F2%29+7%5E2%2A+3.6059
A=88.345