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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

4. Surface Areas and Volumes of Similar Solids

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Exercise 3 Page 450

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

288π ≈ 904.8 cubic millimeters

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 12millimeters. Therefore, the radius is 12÷ 2=6millimeters. We can substitute this value for r in the above formula and simplify the right-hand side.

V=4/3π r^3

r= 6

V=4/3π ( 6)^3

▼

Evaluate right-hand side

Calculate power

V=4/3π (216)

CommutativePropMult

Commutative Property of Multiplication

V=4/3(216)π

MoveRightFacToNum

a/c* b = a* b/c

V=864/3π

Factor out 3

V=3(288)/3π

CancelCommonFac

Cancel out common factors

V=3(288)/3π

Simplify quotient

V=288π

Use a calculator

V=904.778684...

Round to 1 decimal place(s)

V≈ 904.8

The volume of the sphere is 288π cubic millimeters or about 904.8 cubic millimeters.

Subchapter links

Try It p.446-448

Self-Assessment for Concepts & Skills p.448

Self-Assessment for Problem Solving p.449

Review & Refresh p.450