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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 18 Page 443

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

3.5 feet

Practice makes perfect

The volume of a sphere is four thirds the product of π and the cube of the radius. V=4/3π r^3 We want to find the radius of a sphere whose volume is 180 cubic feet. Therefore, we can substitute 180 for V in the above formula and solve it for r.

V=4/3π r^3

V= 180

180=4/3π r^3

▼

Evaluate right-hand side

MoveRightFacToNum

a/c* b = a* b/c

180=4 π r^3/3

LHS * 3=RHS* 3

3* 180 = 3 * 4 π r^3/3

DenomMultFracToNumber

3 * a/3= a

3* 180 = 4 π r^3

Multiply

540 = 4 π r^3

.LHS /4π.=.RHS /4π.

540/4π=4 π r^3/4π

Cross out common factors

540/4π=4π r^3/4π

Simplify quotient

540/4π=r^3

sqrt(LHS)=sqrt(RHS)

sqrt(540/4π)=sqrt(r^3)

RootPowToNumber

sqrt(a^3)=a

sqrt(540/4π)=r

Rearrange equation

r=sqrt(540/4π)

Use a calculator

r=3.502632...

Round to 1 decimal place(s)

r≈ 3.5

The radius of the sphere, correct to the nearest tenth, is 3.5 feet.

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