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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
6. Surface Areas and Volumes of Spheres
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Exercise 27 Page 853

Use the formula for the surface area of a sphere.

About 860 289.5 cubic feet

Practice makes perfect

The top of the Reunion Tower in Dallas, Texas, can be modeled by the following sphere with a surface area of about 13 924Ï€ square feet.

We are asked to find the volume of the top. Let r denote the radius of the sphere. First, let's use the formula for the surface area of a sphere to find its radius, r.

S=4Ï€ r^2
Substitute

S= 13 924Ï€

13 924Ï€ =4Ï€ r^2
â–¼
Solve for r
RearrangeEqn

Rearrange equation

4Ï€ r^2 = 13 924Ï€
DivEqn

.LHS /4Ï€.=.RHS /4Ï€.

r^2=13 924Ï€/4Ï€
ReduceFrac

a/b=.a /Ï€./.b /Ï€.

r^2=13 924/4
CalcQuot

Calculate quotient

r^2=3481
SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(r^2)=sqrt(3481)
SqrtPowToNumber

sqrt(a^2)=a

r=sqrt(3481)
CalcRoot

Calculate root

r=59

Now, let's use the formula for the volume of a sphere. Then we will round the answer to the nearest tenth.

V=4/3Ï€ r^3
â–¼
Substitute 59 for r and evaluate
Substitute

r= 59

V=4/3Ï€ ( 59)^3
CalcPowProd

Calculate power and product

V=4/3* 205 379Ï€
MoveRightFacToNum

a/c* b = a* b/c

V=4(205 379Ï€)/3
Multiply

Multiply

V=821 516Ï€/3
UseCalc

Use a calculator

V=860 289.54346882...
RoundDec

Round to 1 decimal place(s)

V≈ 860 289.5

We found that the volume of the top of the Reunion Tower is about 860 289.5 cubic feet.

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Exercises 2 (Page 852)
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57 engineering
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