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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 19 Page 818

Use the formula for the surface area of a cylinder.

Lateral Area: ≈ 282.7 mm^2
Surface Area: ≈ 339.3 mm^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. Since we are given that the radius is 3mm and the height is 15 mm, we can substitute them into the formula and calculate L.

L=2 π r h

r= 3, h= 15

L=2 π ( 3)( 15)

Multiply

L=90 π

Use a calculator

L=282.743338...

Round to 1 decimal place(s)

L≈ 282.7

The lateral area of the cylinder is 90 π mm^2 that is approximately 282.7mm^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 3 and L with 90 π into the formula, we can calculate S. Let's do it!

S=L+2π r^2

r= 3, L= 90 π

S=90 π+2π( 3)^2

▼

Evaluate right-hand side

Calculate power

S=90 π+2π(9)

Multiply

S=90 π+18π

Add terms

S= 108 π

Use a calculator

S=339.292006 ...

Round to 1 decimal place(s)

S≈ 339.3

The surface area of the cylinder is about 339.3 mm^2.

Subchapter links

Exercises p.817-821