Question

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

Answer 1

Answer:

Area of circle is $\dfrac{225n^{2}}{4\pi} cm^{2}$

Step-by-step 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 $2\pi$

$\dfrac{15n}{2\pi}=\dfrac{2\pi r}{2\pi}$

Simplifying,

$\dfrac{15n}{2\pi}=r$

Formula for area of circle is given as,

$A=\pi r^{2}$

Substituting the value of r,

$A=\pi \left(\dfrac{15n}{2\pi}\right)^{2}$

Squaring the parenthesis,

$A=\pi \left(\dfrac{225n^{2}}{4\pi^{2}}\right)$

Cancelling out the common term,

$A=\dfrac{225n^{2}}{4\pi}$

Therefore, area of circle in terms of n is $A=\dfrac{225n^{2}}{4\pi} cm^{2}$