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McGraw Hill Integrated II, 2012 View details

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Exercise 20 Page 875

The traffic cone is modeled by the following cone with a height of h = 19 inches and a radius of r= 5 inches.

We are asked to find the lateral area of the traffic cone. The lateral area of a cone is L=π r l, where r is the radius and l is the slant height of the cone. Let's use the Pythagorean Theorem for the right triangle to find l.

r^2+ h^2= l^2

SubstituteII

r= 5, h= 19

5^2+ 19^2= l^2

▼

Solve for l

CalcPow

Calculate power

25+361= l^2

AddTerms

Add terms

386= l^2

RearrangeEqn

Rearrange equation

l^2=386

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(l^2)=sqrt(386)

SqrtPowToNumber

sqrt(a^2)=a

l=sqrt(386)

UseCalc

Use a calculator

l=19.6468827...

RoundDec

Round to 2 decimal place(s)

l≈ 19.65

The slant height is about 19.65 inches. Now, let's find the lateral area of the traffic cone.

L=π r l

▼

Substitute values and evaluate

SubstituteII

r= 5, l= 19.65

L=π( 5)( 19.65)

Multiply

L=98.25π

UseCalc

Use a calculator

L=308.661478...

RoundDec

Round to 2 decimal place(s)

L≈ 308.66

The lateral area of the traffic cone is about 308.66 square inches.

From Point A we get that the lateral area is L=308.66 square inches. To get the surface area of the traffic cone we will add the area of the base B to the lateral area. The base is a circle with a radius of r= 5 inches. Now, let's find B using the formula for the area of a circle.

B=π r^2

▼

Substitute 5 for r and evaluate

Substitute

r= 5

B=π( 5)^2

CalcPowProd

Calculate power and product

B=25π

UseCalc

Use a calculator

B=78.539816...