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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Surface Areas of Pyramids and Cones

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Exercise 26 Page 828

Find the lateral area of a cone and the lateral area of a cylinder.

About 311.2 square feet

Practice makes perfect

The given tent can be modeled by the following figure.

We are asked to find its lateral area. It consists of two parts.

The lateral area of a cylinder with a radius of r= 5 feet and a height of h=12-6= 6 feet.
The lateral area of a cone with a radius of r= 5 feet and a slant height of l.

First, let's find the slant height of the cone using the Pythagorean Theorem for right △ ABC.

AB^2+AC^2=BC^2

Substitute AB= 5, AC= 6, BC= l

5^2+ 6^2= l^2

▼

Solve for l

Calculate power

25+36= l^2

Add terms

61= l^2

Rearrange equation

l^2=61

sqrt(LHS)=sqrt(RHS)

l=sqrt(61)

Use a calculator

l=7.810249...

Round to 2 decimal place(s)

l≈ 7.81

Now, let's find the lateral areas.

Figure	Cylinder	Cone
Radius	r= 5	r= 5
Height	h= 6	h= 6
Slant Height	-	l= 7.81
Lateral Area	L=2π r h	L=π r l
Lateral Area	L=2π( 5)( 6)≈ 188.50	L=π( 5)( 7.81)≈ 122.68

Therefore, the lateral area of the cylinder is about 188.50 ft^2 and the lateral area of the cone is about 122.68 ft^2. This tells us that the lateral area of the tent is 188.50+122.68=311.18 ft^2. Since we are asked to round the answer to the nearest tenth, the answer is about 311.18≈311.2 ft^2.

Subchapter links

Exercises p.827-830