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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

2. Surface Areas of Prisms and Cylinders

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Exercise 22 Page 818

Use the formula for the surface area of a cylinder.

Lateral Area: 12.4 cm^2
Surface Area: 32.8 cm^2

Practice makes perfect

We are asked to find the lateral area and surface area of the given cylinder.

We will do these things one at a time.

Lateral Area

Let's recall the formula for the lateral area L of a right cylinder. L=2π rh Here, r is the radius of the base, and h is the height of the cylinder. Let's start by finding the radius of the base. In the diagram, we see that the base is a circle with diameter equal to 3.6 cm. Its radius is exactly the half of the length of the diameter. r = 3.6/2 ⇒ r = 1.8 We also see in the diagram that the height of the solid is 1.1cm. With this information, we can find the lateral area of the prism.

L=2 π r h

r= 1.8, h= 1.1

L=2 π ( 1.8)( 1.1)

Multiply

L=3.96 π

Use a calculator

L=12.440706...

Round to 1 decimal place(s)

L≈ 12.4

The lateral area of the cylinder is 12.4cm^2.

Surface Area

Let's recall the formula for the surface area of a cylinder. S=L+2π r^2 In this formula, r is the radius of the base and L is the lateral area of the cylinder. Substituting r with 1.8 and L with 12.4 into the formula, we can calculate S. Let's do it!

S=L+2π r^2

r= 1.8, L= 12.4

S=12.4+2π( 1.8)^2

▼

Evaluate right-hand side

Calculate power

S=12.4+2π(3.24)

Multiply

S=12.4+6.48π

Use a calculator

S = 12.4+ 20.357520 ...

Round to 1 decimal place(s)

S≈ 12.4 + 20.4

Add terms

S≈ 32.8

The surface area of the cylinder is about 32.8 cm^2.

Subchapter links

Exercises p.817-821