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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 5 Page 441

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

17 157.3cm^3

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 diameter is 32 centimeters. Therefore, the radius is 32÷ 2=16 centimeters. We can substitute this value for r in the above formula and simplify the right-hand side

V=4/3π r^3

r= 16

V=4/3π ( 16)^3

▼

Evaluate right-hand side

Calculate power

V=4/3π (4096)

CommutativePropMult

Commutative Property of Multiplication

V=4/3(4096)π

MoveRightFacToNum

a/c* b = a* b/c

V=4 * 4096/3π

Multiply

V=16 384/3π

Use a calculator

V=17 157.28468

Round to 1 decimal place(s)

V≈ 17 157.3

The volume of the sphere, correct to the nearest tenth, is 17 157.3 cubic centimeters.

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