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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Cumulative Standards Review

Exercise 19 Page 758

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

9/2 π m^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 We are told that the circumference is 3 π cm. Let's use the formula for the circumference C of a circle to find the radius r.

C=2π r

C= 3π

3 π=2π r

.LHS /2π.=.RHS /2π.

3π/2π=r

a/b=.a /π./.b /π.

3/2=r

Rearrange equation

r=3/2

Let's now substitute 32 for r in the formula for the volume and simplify the right-hand side.

V=4/3π r^3

r= 3/2

V=4/3π ( 3/2)^3

▼

Simplify right-hand side

(a/b)^m=a^m/b^m

V=4/3π (3^3/2^3)

Calculate power

V=4/3π (27/8)

CommutativePropMult

Commutative Property of Multiplication

V=4/3(27/8)π

Multiply fractions

V=108/24π

a/b=.a /12./.b /12.

V=9/2π

The volume of the sphere is 92π cm^3.