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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

5. Rewriting Equations and Formulas

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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 = 2 π r

To calculate the radius, we should first isolate it in the formula.

C = 2 π r

$LHS / 2 π = RHS / 2 π$

\frac{C}{2 π} = \frac{2 π r}{2 π}

Simplify quotient

\frac{C}{2 π} = r

Rearrange equation

r = \frac{C}{2 π}

We found that the formula for the radius given the circumference is

r = \frac{C}{2 π} .

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 = \frac{C}{2 π}

Let's start with

C = 7 .

r = \frac{C}{2 π}

$C = 7$

r = \frac{7}{2 π}

Use a calculator

r = 1.114084 \dots

Round to $1$ decimal place(s)

r \approx 1.1

The radius of the given column is approximately

1.1

feet. We can summarize all the other findings in a table.

$C$	$\frac{C}{2 π}$	$r$
$7$	$\frac{7}{2 π}$	$1.1$
$8$	$\frac{8}{2 π}$	$1.3$
$9$	$\frac{9}{2 π}$	$1.4$

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 = \frac{C}{2 π}

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