Answer:
Area of circle is [tex]\dfrac{225n^{2}}{4\pi} cm^{2}[/tex]
Step-by-step explanation:
Formula for circumference of circle is given as,
[tex]C=2\pi r[/tex]
Given that C = 15 n cm,
Substituting the value,
[tex]15n=2\pi r [/tex]
Solving above equation for r, divide both side by [tex] 2\pi [/tex]
[tex]\dfrac{15n}{2\pi}=\dfrac{2\pi r}{2\pi}[/tex]
Simplifying,
[tex]\dfrac{15n}{2\pi}=r[/tex]
Formula for area of circle is given as,
[tex]A=\pi r^{2}[/tex]
Substituting the value of r,
[tex]A=\pi \left(\dfrac{15n}{2\pi}\right)^{2}[/tex]
Squaring the parenthesis,
[tex]A=\pi \left(\dfrac{225n^{2}}{4\pi^{2}}\right)[/tex]
Cancelling out the common term,
[tex]A=\dfrac{225n^{2}}{4\pi}[/tex]
Therefore, area of circle in terms of n is [tex]A=\dfrac{225n^{2}}{4\pi} cm^{2}[/tex]
