Exercise 81 Page 460

Practice makes perfect

a The area of a circle is calculated by multiplying the square of the radius by π.

A=π r^2

Substitute

r= 10

A=π( 10)^2

CalcPow

Calculate power

A=π(100)

CommutativePropMult

Commutative Property of Multiplication

A=100π

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= 7

C=( 7)π

Multiply

C=7π

c To calculate the diameter of a circle we first need to find its radius, r. By substituting the area in the equation A=π r^2, we can solve for the radius r.

A=π r^2

Substitute

A= 121π

121π=π r^2

DivEqn

.LHS /π.=.RHS /π.

121=r^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

11=r

RearrangeEqn

Rearrange equation

r=11

The diameter of a circle is twice its radius. Since we know the radius, we can find the diameter.

d = 2r

Substitute

r= 11

d =22

d 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= 20π

20π=2rπ

DivEqn

.LHS /2π.=.RHS /2π.

10 = r

RearrangeEqn

Rearrange equation

r=10

Let's substitute the radius into the formula for a circle's area.

A=π r^2