Question

if radius cicumference ,area of circle are r, c,and a respectively then prove A
$a = 1 \div 2cr$

Answer 1

Given

Radius :- r

Circumference :- c

Area = a


then as we know that


Circumference of a circle = 2πr ...........(i)

Area of a circle = π r × r .............(i)

then by using equation i & ii

Area of a circle = $\frac{cr}{2}$

HENCE PROVED

Answer 2

Hence proved $a=\frac{1}{2}cr$.

Step-by-step explanation:

Given : If radius circumference, area of circle are r, c,and a respectively.

To prove : $a=\frac{1}{2}cr$  

Solution :

We know that,

The circumference of circle is $c=2\pi r$ ...(1)

The area of the circle is $a=\pi r^2$ ....(2)

Substitute the value of $\pi$ from (1) i.e. $\pi=\frac{c}{2r}$ in (2),

$a=\frac{c}{2r}\times r^2$

$a=\frac{c}{2}\times r$

$a=\frac{1}{2}cr$

Hence proved.

#Learn more

The cicumference of a circle is 31.4cm. find the radius and the and the area of the circle? (take pi= 3.14) explain .

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