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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 10 Page 606

Recall the formula for finding the area of a circle.

52 cm

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 676 π cm^2. By substituting 676 π for A in the formula, we can calculate r.

A=π r^2

A= 676 π

676 π=π r^2

.LHS /π.=.RHS /π.

676 π/π = r^2

a/b=.a /π./.b /π.

676 = r^2

Rearrange equation

r^2 = 676

sqrt(LHS)=sqrt(RHS)

sqrt(r^2) = sqrt(676)

Calculate root

r = ± 26

The radius of the circle is a measurement and therefore cannot be negative, so we will only use the positive result. Thus the radius of the circle is 26 cm. 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(26) D = 52 The diameter of the circle is 52 cm.

Subchapter links

Communicate Your Answer p.601

Monitoring Progress p.602-605