The larger circle has center O and passes through D. The smaller circle has diameter OD. What percent of the larger circle's area is gray?

AdminMod2
Aug 18, 2017

#1**+3 **

gray circle area | = | π | * | (radius)^{2} | ||

radius of the smaller circle = \(\frac{OD}{2}\) | ||||||

gray circle area | = | π | * | (\(\frac{OD}{2}\))^{2} | ||

gray circle area | = | π | * | \(\frac{OD^2}{4}\) | ||

gray circle area | = | \(\frac{πOD^2}{4}\) |

larger circle area | = | π | * | (radius)^{2} | ||

radius of the larger circle = OD | ||||||

larger circle area | = | π | * | OD^{2} |

What, percent, is the gray circle's area out of the larger circle's area?

\(\frac{\text{gray circle area}}{\text{larger circle area}}\,=\,\frac{\frac{\pi OD^2}{4}}{\pi OD^2}\,=\,\frac{\pi OD^2}{4}\,*\,\frac{1}{\pi OD^2}\,=\,\frac14\,=\,\frac{25}{100}\,=\,25\%\)

hectictar
Aug 18, 2017

#1**+3 **

Best Answer

gray circle area | = | π | * | (radius)^{2} | ||

radius of the smaller circle = \(\frac{OD}{2}\) | ||||||

gray circle area | = | π | * | (\(\frac{OD}{2}\))^{2} | ||

gray circle area | = | π | * | \(\frac{OD^2}{4}\) | ||

gray circle area | = | \(\frac{πOD^2}{4}\) |

larger circle area | = | π | * | (radius)^{2} | ||

radius of the larger circle = OD | ||||||

larger circle area | = | π | * | OD^{2} |

What, percent, is the gray circle's area out of the larger circle's area?

\(\frac{\text{gray circle area}}{\text{larger circle area}}\,=\,\frac{\frac{\pi OD^2}{4}}{\pi OD^2}\,=\,\frac{\pi OD^2}{4}\,*\,\frac{1}{\pi OD^2}\,=\,\frac14\,=\,\frac{25}{100}\,=\,25\%\)

hectictar
Aug 18, 2017