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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
5. Volumes of Pyramids and Cones
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Exercise 6 Page 844

Use the formula for the volume of a cone.

164.9cm^3

Practice makes perfect

To calculate the volume of a cone, we can use the following formula. V= 13Ï€ r^2 h Here r is the radius and h is the height of the cone. We are given that the height of the cone is 11.5cm. Let's look at the triangle including the height and the radius of the cone.

Notice that we can find r using the tangent ratio. tan 18^(∘)=r/11.5 Let's solve above equation for r.

tan18^(∘)=r/11.5
â–¼
Solve for r
MultEqn

LHS * 11.5=RHS* 11.5

11.5tan18^(∘)=r
RearrangeEqn

Rearrange equation

r=11.5tan18^(∘)
UseCalc

Use a calculator

r=3.73658...
RoundDec

Round to 1 decimal place(s)

r≈ 3.7

The radius of the cone's base is approximately 3.7 centimeters. Now we have all values to calculate the volume.

V=1/3Ï€ r^2 h
SubstituteII

r= 3.7, h= 11.5

V=1/3Ï€ ( 3.7)^2 ( 11.5)
â–¼
Simplify right-hand side
CalcPow

Calculate power

V=1/3Ï€(13.69)(11.5)
UseCalc

Use a calculator

V=164.866...
RoundDec

Round to 1 decimal place(s)

V≈ 164.9

The volume of the cone is approximately 164.9cm^3.

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