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McGraw Hill Integrated II, 2012 View details

5. Volumes of Pyramids and Cones

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Exercise 33 Page 846

Use the formula for the volume of a cone.

14in.

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To calculate the volume of a cone, we can use the following formula. In this formula r is the radius, and h is the height of a cone. V= 13π r^2 hWe are given that the height of the cone is 12in and the volume is 196π in^3. Let's substitute these values into the above formula and solve the equation for r.

V=1/3π r^2 h

SubstituteII

V= 196π, h= 12

196π=1/3π r^2 ( 12)

▼

Simplify right-hand side

CommutativePropMult

Commutative Property of Multiplication

196π=121/3π r^2

MoveLeftFacToNumOne

a* 1/b= a/b

196π=12/3π r^2

CalcQuot

Calculate quotient

196π=4π r^2

DivEqn

.LHS /4π.=.RHS /4π.

196π/4π=r^2

ReduceFrac

a/b=.a /π./.b /π.

196/4=r^2

CalcQuot

Calculate quotient

49=r^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

7=r

RearrangeEqn

Rearrange equation

r=7

Note that, when solving the above equation, we only needed to consider the principal root because r is a positive number. We found that the radius of our cone is 7 inches. Finally let's recall that the diameter is twice as long as radius. d=2( 7)=14 The diameter of the cone is 14 inches.

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Exercises p.844-847

Exercise 33 Page 846

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