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Big Ideas Math: Modeling Real Life, Grade 8
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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=4/3Ï€ r^3
Substitute

V= 36Ï€

36Ï€=4/3Ï€ r^3
â–¼
Evaluate right-hand side
MoveRightFacToNum

a/c* b = a* b/c

36π=4 π r^3/3
MultEqn

LHS * 3=RHS* 3

3* 36π = 3 * 4 π r^3/3
DenomMultFracToNumber

3 * a/3= a

3* 36π = 4 π r^3
Multiply

Multiply

108π = 4 π r^3
DivEqn

.LHS /4Ï€.=.RHS /4Ï€.

108π/4π=4 π r^3/4π
CrossCommonFac

Cross out common factors

108Ï€/4Ï€=4Ï€ r^3/4Ï€
SimpQuot

Simplify quotient

108/4=r^3
CalcQuot

Calculate quotient

27 =r^3
RadicalEqn

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
RearrangeEqn

Rearrange equation

r=3

The radius of the sphere is 3 meters.

Subchapter links expand_more
arrow_right Try It p.440-441
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Try It 2 (Page 440)
Try It 3 (Page 441)
Try It 4 (Page 441)
arrow_right Self-Assessment for Concepts & Skills p.441
Self-Assessment for Concepts & Skills 5 (Page 441)
Self-Assessment for Concepts & Skills 6 (Page 441)
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arrow_right Self-Assessment for Problem Solving p.442
Self-Assessment for Problem Solving 8 (Page 442)
Self-Assessment for Problem Solving 9 (Page 442)
arrow_right Review & Refresh p.443
Review & Refresh 1 (Page 443)
Review & Refresh 2 (Page 443)
Review & Refresh 3 (Page 443)
Review & Refresh 4 (Page 443)
Review & Refresh 5 (Page 443)
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arrow_right Concepts, Skills, & Problem Solving p.443-444
Concepts, Skills, & Problem Solving 7 (Page 443)
Concepts, Skills, & Problem Solving 8 (Page 443)
Concepts, Skills, & Problem Solving 9 (Page 443)
Concepts, Skills, & Problem Solving 10 (Page 443)
Concepts, Skills, & Problem Solving 11 (Page 443)
Concepts, Skills, & Problem Solving 12 (Page 443)
Concepts, Skills, & Problem Solving 13 (Page 443)
Concepts, Skills, & Problem Solving 14 (Page 443)
Concepts, Skills, & Problem Solving 15 (Page 443)
Concepts, Skills, & Problem Solving 16 (Page 443)
Concepts, Skills, & Problem Solving 17 (Page 443)
Concepts, Skills, & Problem Solving 18 (Page 443)
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Concepts, Skills, & Problem Solving 22 (Page 444)
Concepts, Skills, & Problem Solving 23 (Page 444)
Concepts, Skills, & Problem Solving 24 (Page 444)
Concepts, Skills, & Problem Solving 25 (Page 444)
Concepts, Skills, & Problem Solving 26 (Page 444)
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