Respuesta :
Answer:
The relation for the area of circle with radius , Diameter , circumference is
A= [tex]\pi[/tex] × radius²
A = [tex]\frac{\pi D^{2} }{4}[/tex]
A = [tex]\frac{c^{2} }{4\pi }[/tex]
Step-by-step explanation:
Given as :
The formula for the area of circle = [tex]\pi[/tex] × radius²
I.e A = [tex]\pi[/tex] × radius²
Now If we know radius then
Area calculated as A= [tex]\pi[/tex] × radius²
If we know Diameter then
Area calculated as [tex]\pi[/tex] × ([tex]\dfrac{\textrm Diameter}{2}[/tex])²
Or, A = [tex]\pi[/tex] × ([tex]\dfrac{\textrm D}{2}[/tex])²
I,e A = [tex]\frac{\pi D^{2} }{4}[/tex]
If we know the circumference then
∵ circumference = c = 2 × [tex]\pi[/tex] × radius
or, c = 2 × [tex]\pi[/tex] × r
from here we calculate radius
I.e r = [tex]\frac{c}{2\pi }[/tex]
And So , Area ( A ) = [tex]\pi[/tex] × radius²
I.e A = [tex]\pi[/tex] × ( [tex]\frac{c}{2\pi }[/tex] )²
Or, A = [tex]\frac{c^{2} }{4\pi }[/tex]
Hence The relation for the area of circle with radius , Diameter , circumference is
A= [tex]\pi[/tex] × radius²
A = [tex]\frac{\pi D^{2} }{4}[/tex]
A = [tex]\frac{c^{2} }{4\pi }[/tex] Answer
