Question

The circumference of a circle is 15n cm what is the area of the circle in terms of n

Answer 1

Area of circle is
`(225n^(2))/(4\pi) cm^(2)`

Explanation:

Formula for circumference of circle is given as,

`C=2\pi r`

Given that C = 15 n cm,

Substituting the value,

`15n=2\pi r`

Solving above equation for r, divide both side by
`2\pi`

`(15n)/(2\pi)=(2\pi r)/(2\pi)`

Simplifying,

`(15n)/(2\pi)=r`

Formula for area of circle is given as,

`A=\pi r^(2)`

Substituting the value of r,

`A=\pi \left((15n)/(2\pi)\right)^(2)`

Squaring the parenthesis,

`A=\pi \left((225n^(2))/(4\pi^(2))\right)`

Cancelling out the common term,

`A=(225n^(2))/(4\pi)`

Therefore, area of circle in terms of n is
`A=(225n^(2))/(4\pi) cm^(2)`