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Serena is wearing a pendant that was made by inscribing a square ruby in a sterling silver circle. The distance from the center of the pendant to its edge is 5.3 centimeters. Find the area of the pendant that is not covered by the ruby. Round to the nearest hundredth

Guest Mar 31, 2017
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Guest Mar 31, 2017
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"Serena is wearing a pendant that was made by inscribing a square ruby in a sterling silver circle. The distance from the center of the pendant to its edge is 5.3 centimeters. Find the area of the pendant that is not covered by the ruby. Round to the nearest hundredth"

 

radius of circle: r = 5.3cm

 

Area of circular part of pendant;  A1 = pi*r2 so A1 = pi*5.32 cm2

 

r is half the diagonal of the square ruby so the side length of the square is 2r/sqrt(2) → r*sqrt(2) 

Area of square ruby is:  A2 = (r*sqrt(2))2 or A2 = 2*5.32 cm2

 

Area not covered by ruby:  A1 - A2 = (pi - 2)*5.32 cm2 →    32.07 cm2

.

Alan  Mar 31, 2017

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