Exercise 11 Page 213

We are given the following net.

This net represents the cylinder shown below.

To calculate the area of the complex figure, we can first calculate the area of the two circles and rectangle. Then we will add the areas we find. Since the circles have the same radius their areas are the same. Let's represent the area of the net with an equation.

A_(net)=2A_(circle)+A_(rectangle)

Area of the Circle

We can calculate the area of the circle using the following formula. A_(circle)=π r^2 We are given that the radius of the circle is 6 cm. Let's substitute 6 for r and calculate A_(circle).

A_(circle)=π r^2

SubstituteII

r= 6, π= 3.14

A_(circle)= 3.14 * 6^2

CalcPow

Calculate power

A_(circle)=3.14* 36

Multiply

Multiply

A_(circle)=113.04

RoundInt

Round to nearest integer

A_(circle)=113

The area of each circle is 113 cm^2.

Area of the Rectangle

Let's calculate the area of the rectangle. A_(rectangle)=lw Here, l is the length and w is the width. We are given that the width equals 8 cm. What about the length? From the diagram, we can see that the rectangle's length is the same as the circumference of the given circles. Thus, if we calculate the circumference of the circle, we will find the length of the rectangle. Let's use the following formula. C=2π r We can substitute r with 6 and calculate C.

C=2π r

SubstituteII

r= 6, π= 3.14

C=2* 3.14 * 6

Multiply

Multiply

C=37.68

RoundDec

Round to 1 decimal place(s)

C=37.7

Thus, the length of the rectangle is 37.7 cm. Now we are able to calculate the area of the rectangle. To do that, we substitute l with 37.7 and w with 8 into the above formula.

A_(rectangle)=lw

SubstituteII

l= 37.7, w= 8

A_(rectangle)= 37.7* 8

Multiply

Multiply

A_(rectangle)=301.6

Hence, the area of the rectangle is 301.6 cm^2.

Area of the Net

Now that we know the area of the rectangle and the circles, we can add them and find the area of the net.

A_(net)=2A_(circle)+A_(rectangle)

SubstituteII

A_(circle)= 113, A_(rectangle)= 301.6

A_(net)=2* 113+ 301.6

Multiply

Multiply

A_(net)=226+301.6

AddTerms

Add terms

A_(net)=527.6

RoundInt

Round to nearest integer

A_(net)=528

The area of the net is 528 cm^2.