Exercise 32 Page 612

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

Circumference: about 18.8ft
Area: about 28.3ft^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.

From the figure, we know that the radius of the circle is 3ft. We can substitute this value for r in the formula for the circumference of a circle and simplify.

C=2π r

Substitute

r= 3

C=2π( 3)

CommutativePropMult

Commutative Property of Multiplication

C=2(3)π

Multiply

C=6π

UseCalc

Use a calculator

C=18.849555...

RoundDec

Round to 1 decimal place(s)

C≈ 18.8

The circumference of the circle is approximately 18.8ft.

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 3ft. By substituting 3 for r in the formula, we can calculate A.

A=π r^2

Substitute

r= 3

A=π( 3)^2

CalcPow

Calculate power

A=π(9)

CommutativePropMult

Commutative Property of Multiplication

A=9π

UseCalc

Use a calculator