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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

3. Volumes of Spheres

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Exercise 3 Page 441

The volume of a sphere is four thirds the product of π and the cube of the radius.

3 m

Practice makes perfect

Consider the given sphere.

The volume of a sphere is four thirds the product of π and the cube of the radius. V=4/3π r^3 In the diagram we can see that the volume is 36π cubic meters. Therefore, we can substitute 36π for V in the above formula and solve it for r.

V=4/3π r^3

V= 36π

36π=4/3π r^3

▼

Evaluate right-hand side

MoveRightFacToNum

a/c* b = a* b/c

36π=4 π r^3/3

LHS * 3=RHS* 3

3* 36π = 3 * 4 π r^3/3

DenomMultFracToNumber

3 * a/3= a

3* 36π = 4 π r^3

Multiply

108π = 4 π r^3

.LHS /4π.=.RHS /4π.

108π/4π=4 π r^3/4π

Cross out common factors

108π/4π=4π r^3/4π

Simplify quotient

108/4=r^3

Calculate quotient

27 =r^3

sqrt(LHS)=sqrt(RHS)

sqrt(27)=sqrt(r^3)

SplitIntoFactors

Split into factors

sqrt(3* 3* 3)=sqrt(r^3)

ProdToPowThreeFac

a* a* a=a^3

sqrt(3^3)=sqrt(r^3)

RootPowToNumber

sqrt(a^3)=a

3=r

Rearrange equation

r=3

The radius of the sphere is 3 meters.

Subchapter links

Try It p.440-441

Self-Assessment for Concepts & Skills p.441

Self-Assessment for Problem Solving p.442

Review & Refresh p.443

Concepts, Skills, & Problem Solving p.443-444