Question

The formula for the area of a circle is A equals xr2 this formula allows you to find the area of a circle if you know the radius or diameter how can you find the area if you only know the circumference write the formula for the circumference using our then solve for r

Answer 1

The relation for the area of circle with radius , Diameter , circumference is

A=
`\pi` × radius²

A =
`(\pi D^(2) )/(4)`

A =
`(c^(2) )/(4\pi )`

Explanation:

Given as :

The formula for the area of circle =
`\pi` × radius²

I.e A =
`\pi` × radius²

Now If we know radius then

Area calculated as A=
`\pi` × radius²

If we know Diameter then

Area calculated as
`\pi` × (
`(\textrm Diameter)/(2)`)²

Or, A =
`\pi` × (
`(\textrm D)/(2)`)²

I,e A =
`(\pi D^(2) )/(4)`

If we know the circumference then

∵ circumference = c = 2 ×
`\pi` × radius

or, c = 2 ×
`\pi` × r

from here we calculate radius

I.e r =
`(c)/(2\pi  )`

And So , Area ( A ) =
`\pi` × radius²

I.e A =
`\pi` × (
`(c)/(2\pi  )` )²

Or, A =
`(c^(2) )/(4\pi )`

Hence The relation for the area of circle with radius , Diameter , circumference is

A=
`\pi` × radius²

A =
`(\pi D^(2) )/(4)`

A =
`(c^(2) )/(4\pi )` Answer