Question

what is the ratio of the sector area to the area of the entire circle?
options:
$\frac{1}{5}$
$\frac{1}{2}$
2
4
(there is a circle with center n, radius 4, and a sector lnm with central angle 72°)

Explanation:

Step1: Recall the ratio formula for sector and circle area.

The ratio of the sector area to the circle area is equal to the ratio of the sector's central angle to the total angle in a circle (360°). So the formula is $\frac{\text{Central Angle of Sector}}{360^\circ}$.

Step2: Substitute the given central angle.

The central angle of the sector is $72^\circ$. So we calculate $\frac{72^\circ}{360^\circ}$.
Simplifying $\frac{72}{360}$, we divide numerator and denominator by 72: $\frac{72\div72}{360\div72}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$ (corresponding to the option $\boldsymbol{\frac{1}{5}}$)