Exercise 6 Page 441

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 4500π cubic yards. Therefore, we can substitute 4500π for V in the above formula and solve it for r.

V=4/3π r^3

Substitute

V= 4500π

4500π=4/3π r^3

▼

Evaluate right-hand side

MoveRightFacToNum

a/c* b = a* b/c

4500π=4 π r^3/3

MultEqn

LHS * 3=RHS* 3

3* 4500π = 3 * 4 π r^3/3

DenomMultFracToNumber

3 * a/3= a

3* 4500π = 4 π r^3

Multiply

13 500π = 4 π r^3

DivEqn

.LHS /4π.=.RHS /4π.

13 500π/4π=4 π r^3/4π

CrossCommonFac

Cross out common factors

13 500π/4π=4π r^3/4π

SimpQuot

Simplify quotient

13 500π/4π=r^3

CalcQuot

Calculate quotient

3375π =r^3

RadicalEqn

sqrt(LHS)=sqrt(RHS)

sqrt(3375π)=sqrt(r^3)

RootPowToNumber

sqrt(a^3)=a

sqrt(3375π)=r

RearrangeEqn

Rearrange equation

r=sqrt(3375π)

UseCalc

Use a calculator

r=21.968878...

RoundDec

Round to 1 decimal place(s)

r≈ 22

The radius of the sphere, correct to the nearest tenth, is 22 yards.