body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math: Modeling Real Life, Grade 8

BI

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

3. Volumes of Spheres

Continue to next subchapter

Exercise 4 Page 441

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

1.5 inches

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 14 cubic inches. Therefore, we can substitute 14 for V in the above formula and solve it for r.

V=4/3π r^3

V= 14

14=4/3π r^3

▼

Evaluate right-hand side

MoveRightFacToNum

a/c* b = a* b/c

14=4 π r^3/3

LHS * 3=RHS* 3

3* 14 = 3 * 4 π r^3/3

DenomMultFracToNumber

3 * a/3= a

3* 14 = 4 π r^3

Multiply

42 = 4 π r^3

.LHS /4π.=.RHS /4π.

42/4π=4 π r^3/4π

Cross out common factors

42/4π=4π r^3/4π

Simplify quotient

42/4π=r^3

sqrt(LHS)=sqrt(RHS)

sqrt(42/4π)=sqrt(r^3)

RootPowToNumber

sqrt(a^3)=a

sqrt(42/4π)=r

Rearrange equation

r=sqrt(42/4π)

Use a calculator

r=1.495132...

Round to 1 decimal place(s)

r≈ 1.5

The radius of the sphere, correct to the nearest tenth, is 1.5 inches.

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