Exercise 30 Page 612

Recall the formulas for finding circumference and the area of a circle.

Circumference: about 11.3in.
Area: about 10.2in.^2

Practice makes perfect

Let's find the circumference and the area of the circle separately.

Circumference

The circumference C of a circle with radius r is calculated using the formula below. C=2π r Let's now consider the given diagram.

In the diagram we can see that the diameter is 3.6inches. Therefore, the radius is 3.6÷ 2= 1.8inches. We can substitute this value for r in the formula for the circumference of a circle and simplify.

C=2π r

Substitute

r= 1.8

C=2π( 1.8)

CommutativePropMult

Commutative Property of Multiplication

C=2(1.8)π

Multiply

C=3.6π

UseCalc

Use a calculator

C=11.309733...

RoundDec

Round to 1 decimal place(s)

C≈ 11.3

The circumference of the circle is approximately 11.3inches.

Area

Similar to the perimeter, the area of a circle with radius r is calculated using the formula below. A=π r^2 We know that the radius of the circle is 1.8m. By substituting 1.8 for r in the formula, we can calculate A.

A=π r^2

Substitute

r= 1.8

A=π( 1.8)^2

CalcPow

Calculate power

A=π(3.24)

CommutativePropMult

Commutative Property of Multiplication

A=3.24π

UseCalc

Use a calculator