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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 20 Page 818

Use the formula for the surface area of a cylinder.

Lateral Area: ≈ 703.7 ft^2
Surface Area: ≈ 1011.6 ft^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 7ft and the height is 16 ft, we can substitute them into the formula and calculate L.

L=2 π r h

r= 7, h= 16

L=2 π ( 7)( 16)

Multiply

L=224π

Use a calculator

L=703.716754...

Round to 1 decimal place(s)

L≈ 703.7

The lateral area of the solid is 703.7 ft^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 7 and L with 703.7 into the formula, we can calculate S. Let's do it!

S=L+2π r^2

r= 7, L= 703.7

S=703.7+2π( 7)^2

▼

Simplify right-hand side

Calculate power

S=703.7+2π(49)

Multiply

S=703.7+98π

Use a calculator

S=703.7 + 307.876080 ...

Round to 1 decimal place(s)

S≈703.7 +307.9

Add terms

S≈ 1011.6

The surface area of the cylinder is about 1011.6 ft^2.

Subchapter links

Exercises p.817-821