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?

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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

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Best Answer

+9466

+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	*	OD²

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

2⁺⁰ Answers

+9466

+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	*	OD²

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

+128408

+2

Thanks, hectictar......!!!!

Another thing to realize is that circles are to one another as the squares of their radiuses.....

Thus.....the smaller circle has a radius of 1/2 the larger circle...so...its area = (1/2)^2 = 1/4 that of the larger circle

CPhill Aug 18, 2017

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