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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

2. Areas of Circles and Sectors

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Exercise 9 Page 606

Recall the formula for finding the area of a circle.

About 4.00 inches

Practice makes perfect

The area of a circle with radius r is calculated using the formula below. A=π r^2We know that the area of the circle is 12.6 in^2. By substituting 12.6 for A in the formula, we can calculate r.

A=π r^2

A= 12.6

12.6=π r^2

.LHS /π.=.RHS /π.

12.6/π = r^2

Rearrange equation

r^2 = 12.6/π

sqrt(LHS)=sqrt(RHS)

sqrt(r^2) = sqrt(12.6/π)

Calculate root

r = ± 2.002674 ⋯

The radius of the circle is a measurement and therefore cannot be negative. This means we will only use the positive result. Rounded to the nearest hundredth, the radius of the circle is approximately 2.00 inches. We know that the diameter of a circle is exactly twice as long as its radius. With that information we can calculate the diameter. D = 2r D = 2(2.00) D = 4.00 The diameter of the circle is approximately 4.00 inches.

Subchapter links

Communicate Your Answer p.601

Monitoring Progress p.602-605