Exercise 96 Page 467

Practice makes perfect

a The circumference of a circle can be calculated by multiplying the diameter, 2r, by π. The area of a circle is calculated by multiplying the square of the radius by π.

C=2rπ

Substitute

r= 14

C=2( 14)π

Multiply

C=28π

Let's also calculate the area.

A=π r^2

Substitute

r= 14

A=π( 14)^2

CalcPow

Calculate power

A=π(196)

CommutativePropMult

Commutative Property of Multiplication

A=196π

b Note that the diameter is the same thing as the radius multiplied by 2. Therefore, with the given information we can find the circle's circumference.

C=2rπ

Substitute

2r= 10

C=( 10)π

Multiply

C=10π

Before we can calculate the area, we have to find the radius by dividing the diameter by 2. radius: 10/2=5 Now we can calculate the area.

A=π r^2

Substitute

r= 5

A=π( 5)^2

CalcPow

Calculate power

A=π(25)

Multiply

A=25π

c To calculate the area of a circle we need to know the radius, r. By substituting the circumference in the equation C=2rπ, we can solve for the radius r.

C=2rπ

Substitute

C= 100π

100π=2rπ

DivEqn

.LHS /2π.=.RHS /2π.

50=r

RearrangeEqn

Rearrange equation

r=50

When we know the radius of the circle, we can find the area.

A=π r^2

Substitute

r= 50

A=π( 50)^2

CalcPow

Calculate power

A=π(2500)

CommutativePropMult

Commutative Property of Multiplication

A=2500π

d To calculate the area of a circle we need to know the radius, r. Let's rearrange the formula that describes the circumference so that it is solved for r.

C=2rπ

DivEqn

.LHS /2π.=.RHS /2π.

C/2π=r

RearrangeEqn

Rearrange equation

r=C/2π

Now we can substitute the expression for the radius into the formula for a circle's area.

A=π r^2

Substitute

r= C/2π

A=π( C/2π)^2