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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 924π 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=4π r^2

S= 13 924π

13 924π =4π r^2

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Solve for r

Rearrange equation

4π r^2 = 13 924π

.LHS /4π.=.RHS /4π.

r^2=13 924π/4π

a/b=.a /π./.b /π.

r^2=13 924/4

Calculate quotient

r^2=3481

sqrt(LHS)=sqrt(RHS)

sqrt(r^2)=sqrt(3481)

SqrtPowToNumber

sqrt(a^2)=a

r=sqrt(3481)

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=4/3π r^3

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Substitute 59 for r and evaluate

r= 59

V=4/3π ( 59)^3

Calculate power and product

V=4/3* 205 379π

MoveRightFacToNum

a/c* b = a* b/c

V=4(205 379π)/3

Multiply

V=821 516π/3

Use a calculator

V=860 289.54346882...

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.

Subchapter links

Exercises p.852-855