Exercise 39 Page 42

Practice makes perfect

a The circumference of a circle is calculated using the following formula, where r is the radius.

C=2π r To calculate the radius, we should first isolate it in the formula.

C=2π r

DivEqn

.LHS /2π.=.RHS /2π.

C/2π=2 π r/2 π

SimpQuot

Simplify quotient

C/2π=r

RearrangeEqn

Rearrange equation

r=C/2π

We found that the formula for the radius given the circumference is r= C2π.

b To calculate the radius of a column given its circumference, we need to substitute this circumference value for C into the formula found in Part A.

r=C/2πLet's start with C = 7.

r=C/2π

Substitute

C= 7

r=7/2π

UseCalc

Use a calculator

r = 1.114084 ...

RoundDec

Round to 1 decimal place(s)

r ≈ 1.1

The radius of the given column is approximately 1.1 feet. We can summarize all the other findings in a table.

C	C/2π	r
7	7/2π	1.1
8	8/2π	1.3
9	9/2π	1.4

c We know that a cross section of a column is a circle. We are asked to explain how we can find the area of a circle when we know its circumference. First, recall the formula for the area of a circle.

A=π r^2 To calculate the area of a circle the only thing we need is its radius. From Part A we know how to find the radius of a circle given the circumference. r=C/2π What we do next is substitute the found radius into the formula for the area of a circle, then evaluate.

Subchapter links

Communicate Your Answer p.35

Monitoring Progress p.36-39

Exercises p.40-42

Exercise 39 Page 42

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