Question

What percent of the total area of the circular disk is colored?

• A. $60\%$
• B. $66.7\%$
• C. $70\%$
• D. $73.50\%$

Answer 1

The correct option is B $66.7\%$

Total area of disk

$A_d=\pi \times r^2$

Angle $t$ in radians of central angle of red sector

$t=(360-120)\times \frac{\pi }{180}=\left(\frac{4}{3}\right)pi$

Area of red sector

$A_s=\left(\frac{1}{2}\right)t\times r^2$

Percentage of total area in red

$P=\frac{[\left(\frac{1}{2}\right)t\times r^2]}{[\pi \times r^2]}$

$=\frac{4}{6}=66.7$% ($3$ significant digits)