the difference between circumference and diameter of a circle is 21.4 cm. Find the radius of the circle
Answers
Answer:
Circle
radius
r=10.7cm
Step-by-step explanation:
Given:-
the difference between circumference and diameter of a circle is 21.4 cm.
To find:-
Find the radius of the circle .
Solution:-
Let the diameter of a circle be "d" units
d=2r units-----(1)
Radius of the circle is r units
and the Circumference of the circle=2πr units
=>C=2πr-----(2)
Now their difference=C-d
=>(2)-(1)
=>2πr-2r
=>2r(π-1)------(3)
as we know π=22/7
substitute the value of π in (3) then we get
=>2r[(22/7)-1]
=>2r(22-7)/7
=>2r(15/7)
=>30r/7
Their difference=30r/7----(4)
But according to the given problem
Their difference is given by 21.4 cm
therefore,
30r/7=21.4
=>30r=21.4×7
=>30r=149.8
=>r=149.8/30
=>r=74.9/15
=>r=4.99 cm(approximately)
Answer:-
The radius of the given circle =4.99 cm
Check:-
The difference between the circumference and the diameter of the circle
=>[2(22/7)(4.99)]-(2×4.99)
=>(2×4.99)[(22/7)-1]
=>(2×4.99)(15/7)
=>30×4.99/7
=>149.8/7
=>21.38(approximately)
=>21.4cm
Verified✅