Exercise 6 Page 622

We want to find the lateral area of the given cylinder.

To do so, we must know that the lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder. Note that the base is congruent to the top face. Therefore, their circumferences are the same. L.A.=2π rh In this formula, r is the radius of the base and h is the height of the cylinder. From the diagram above we can see that the diameter of the base is 6.2 inches. Recall, that the diameter of a circle is twice the length of the radius. With this in mind, we can find the length of the radius by substituting d=6.2 into the formula below.

d=2r

Substitute

d= 6.2

6.2=2r

DivEqn

.LHS /2.=.RHS /2.

6.2/2=2r/2

ReduceFrac

a/b=.a /2./.b /2.

6.2/2=r/1

DivByOne

a/1=a

6.2/2=r

RearrangeEqn

Rearrange equation

r=6.2/2

CalcQuot

Calculate quotient

r=3.1

Finally, by substituting r with 3.1 and h with 6.8 into the formula, we can solve for L.A. Let's do it!

L.A.=2π rh

SubstituteII

r= 3.1, h= 6.8

L.A.=2π( 3.1)( 6.8)

▼

Simplify right-hand side

Multiply

Multiply

L.A.=42.16π

UseCalc

Use a calculator

L.A.=132.449546...

RoundDec

Round to 1 decimal place(s)

L.A.≈ 132.4

The lateral area of the cylinder is about 132.4 square inches.