the circuference of acircle exceeds its diamiter by 30. find the radius.
Answers
c = circumference of a circle = 2 * pi * r
d = diameter of a circle = 2 * r
r = the radius of the circle
the circumference of a circle exceeds its diameter by 30 cm.
this means that:
c = d + 30
substituting for c and d, we get:
2 * pi * r = 2 * r + 30
subtract 2 * r from both sides of the equation to get:
(2 * pi * r) - (2 * r) = 30
factor out the (2 * r) on the left side of the equation to get:
(2 * r) * (pi - 1) = 30
divide both sides of this equation by (pi - 1) to get:
2 * r = 30 / (pi - 1)
divide both sides of this equation by 2 to get:
r = 30 / ((pi - 1) * (2))
solve to get:
r = 7.004133104
this means that:
d = 7.004133104 * 2 = 14.00826621
the circumference of the circle is equal to 2 * pi * r which is equal to 2 * pi * 7.004133104 which is equal to 44.00826621.
the difference between the circumference and the diameter is equal to 44.00826621 - 14.00826621 = 30.
Answer:
Step-by-step explanation:
let the diameter of a circle be x
circumference exceeds the diameter by 30 so
circumference=x+30
Now
radius=half diameter
=d/2
=x/2
Now
circumference=2πr
substituting the value of circumference and the radius which we have
x+30=2×22÷7×x÷2 the value of π is 22÷7 so I have written 22/7
x+30=44x÷14 instead ofπ
doing criss cross multiplication
14(x+30)=44x
14x+420=44x
420=44x-14x
420=30x
x=420÷30
x=14
Now
radius=d÷2
radius =x÷2
radius=14÷2
radius=7