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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
1. Circles and Circumference
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Exercise 58 Page 723

What is the formula for finding the circumference of a circle?

B

Practice makes perfect

We want to find the radius of the circle given in the exercise. The area of a circle with radius r is calculated using the formula below. A=π r^2 From the exercise, we know that the area of the circle is π4square units. By substituting π4 for A in the formula, we can solve for r.

A=Ï€ r^2
Substitute

A= π/4

Ï€/4=Ï€ r^2
DivEqn

.LHS /Ï€.=.RHS /Ï€.

1/4= r^2
RearrangeEqn

Rearrange equation

r^2 = 1/4
RadicalEqn

sqrt(LHS)=sqrt(RHS)

r = sqrt(1/4)
RootQuot

sqrt(a/b)=sqrt(a)/sqrt(b)

r = sqrt(1)/sqrt(4)
CalcRoot

Calculate root

r = 1/2
CalcQuot

Calculate quotient

r = 0.5

Note that since r is the radius, we know that it is a positive number. This is why we keep the principal root when solving the equation. Therefore, the correct answer is B.

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