Holt Mcdougal Larson Algebra 2: Student Edition 2012
Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
Expert Solution & Answer
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Chapter 5.4, Problem 51PS
Solution

a.

To prove: The height h of the cylindrical tank is 43r .

Given information:

Volume of the spherical tank is equal to Volume of the cylindrical tank.

Formula used:

Volume of the sphere: 43πr3

Volume of the cylinder: πr2h

Proof:

Given the:

Volume of the sphere is equal to Volume of the cylinder

Know that the;

Volume of the sphere: 43πr3

Volume of the cylinder: πr2h

So,

  43πr3=πr2h

Factor out r2 ;

  43πr=πh

Factor out π ;

  43r=h

Here, prove that the height h of the cylindrical tank is 43r .

b.

To calculate: The surface area of each tank in terms of r .

The surface area of spherical tank in terms of r is 4πr2 .

The surface area of cylindrical tank in terms of r is 143πr2 .

Given information:

Volume of the spherical tank is equal to Volume of the cylindrical tank.

Formula used:

The surface area of a sphere: 4πr2

The surface area of a cylinder: 2πr2+2πrh

Calculation:

The expression to find the surface area of a sphere, the tower on the left;

The surface area of a sphere: 4πr2

The surface area of a cylinder, the tower on the right;

The surface area of a cylinder: 2πr2+2πrh

The volumes of each water tower are equal:

  43πr3=πr2h

Divide both sides by πr2 ;

  h=43r

So,

  2πr2+2πr43r2πr2+83πr2143πr2

Conclusion:

The surface area of each tank in terms of r : 4πr2;143πr2

c.

To calculate: The ratio of the surface area of the spherical tank to the surface area of the cylindrical tank. Explain what the ratio tells you about which water tower would take less material to build.

The ratio of the surface area of the spherical tank to the surface area of the cylindrical tank is 6:7 . This tells that when building two tanks with the same volume and radius, but with one as a sphere and one as a cylinder, the spherical one will take up less material to build.

Given information:

Volume of the spherical tank is equal to Volume of the cylindrical tank.

Concept used:

The surface area of a sphere: 4πr2

The surface area of a cylinder: 2πr2+2πrh

Calculation:

The surface area of spherical tank = 4πr2 .

The surface area of cylindrical tank = 143πr2

Now,

The ratio of the surface area of the spherical tank to the surface area of the cylindrical tank:

  4πr2143πr2

Cancel πr2 from the numerator and denominator and simplify;

  4143=3×414=1214=67

Conclusion:

The obtained ratio by calculation is 6:7 .

Chapter 5 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 5.1 - Prob. 11GPCh. 5.1 - Prob. 12GPCh. 5.1 - Prob. 13GPCh. 5.1 - Prob. 14GPCh. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10ECh. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37PSCh. 5.1 - Prob. 38PSCh. 5.1 - Prob. 39PSCh. 5.1 - Prob. 40PSCh. 5.1 - Prob. 41PSCh. 5.1 - Prob. 42PSCh. 5.2 - Prob. 1GPCh. 5.2 - Prob. 2GPCh. 5.2 - Prob. 3GPCh. 5.2 - Prob. 4GPCh. 5.2 - Prob. 5GPCh. 5.2 - Prob. 6GPCh. 5.2 - Prob. 7GPCh. 5.2 - 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Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41PSCh. 5.5 - Prob. 42PSCh. 5.5 - Prob. 43PSCh. 5.5 - Prob. 44PSCh. 5.5 - Prob. 45PSCh. 5.5 - Prob. 1PCh. 5.5 - Prob. 2PCh. 5.5 - Prob. 3PCh. 5.5 - Prob. 4PCh. 5.5 - Prob. 5PCh. 5.5 - Prob. 6PCh. 5.5 - Prob. 7PCh. 5.6 - Prob. 1GPCh. 5.6 - Prob. 2GPCh. 5.6 - Prob. 3GPCh. 5.6 - Prob. 4GPCh. 5.6 - Prob. 5GPCh. 5.6 - Prob. 6GPCh. 5.6 - Prob. 7GPCh. 5.6 - Prob. 8GPCh. 5.6 - Prob. 9GPCh. 5.6 - Prob. 10GPCh. 5.6 - Prob. 11GPCh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Prob. 15ECh. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.6 - Prob. 21ECh. 5.6 - Prob. 22ECh. 5.6 - Prob. 23ECh. 5.6 - Prob. 24ECh. 5.6 - Prob. 25ECh. 5.6 - Prob. 26ECh. 5.6 - Prob. 27ECh. 5.6 - Prob. 28ECh. 5.6 - Prob. 29ECh. 5.6 - Prob. 30ECh. 5.6 - Prob. 31ECh. 5.6 - Prob. 32ECh. 5.6 - Prob. 33PSCh. 5.6 - Prob. 34PSCh. 5.6 - Prob. 35PSCh. 5.6 - Prob. 36PSCh. 5.6 - Prob. 37PSCh. 5.6 - Prob. 38PSCh. 5.6 - Prob. 1QCh. 5.6 - Prob. 2QCh. 5.6 - Prob. 3QCh. 5.6 - Prob. 4QCh. 5.6 - Prob. 5QCh. 5.6 - Prob. 6QCh. 5.6 - Prob. 7QCh. 5.6 - Prob. 8QCh. 5.6 - Prob. 9QCh. 5.6 - Prob. 10QCh. 5.6 - Prob. 11QCh. 5.6 - Prob. 12QCh. 5.6 - Prob. 13QCh. 5.6 - Prob. 14QCh. 5.6 - Prob. 1PCh. 5.6 - Prob. 2PCh. 5.6 - Prob. 3PCh. 5.6 - Prob. 4PCh. 5.6 - Prob. 5PCh. 5.6 - Prob. 6PCh. 5.6 - Prob. 7PCh. 5.6 - Prob. 1.1PCh. 5.6 - Prob. 1.2PCh. 5.6 - Prob. 1.3PCh. 5.6 - Prob. 1.4PCh. 5.6 - Prob. 1.5PCh. 5.6 - Prob. 1.6PCh. 5.6 - Prob. 1.7PCh. 5.6 - Prob. 1.8PCh. 5.6 - Prob. 1.9PCh. 5.6 - Prob. 1.10PCh. 5.6 - Prob. 1.11PCh. 5.6 - Prob. 1.12PCh. 5.6 - Prob. 1.13PCh. 5.6 - Prob. 1.14PCh. 5.6 - Prob. 1.15PCh. 5.6 - Prob. 1.16PCh. 5.6 - Prob. 1.17PCh. 5.6 - Prob. 1.18PCh. 5.6 - Prob. 1.19PCh. 5.6 - Prob. 1.20PCh. 5.6 - Prob. 1.21PCh. 5.6 - Prob. 1.22PCh. 5.7 - Prob. 1GPCh. 5.7 - Prob. 2GPCh. 5.7 - Prob. 3GPCh. 5.7 - Prob. 4GPCh. 5.7 - Prob. 5GPCh. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Prob. 6ECh. 5.7 - Prob. 7ECh. 5.7 - Prob. 8ECh. 5.7 - Prob. 9ECh. 5.7 - Prob. 10ECh. 5.7 - Prob. 11ECh. 5.7 - Prob. 12ECh. 5.7 - Prob. 13ECh. 5.7 - Prob. 14ECh. 5.7 - Prob. 15ECh. 5.7 - Prob. 16ECh. 5.7 - Prob. 17ECh. 5.7 - Prob. 18ECh. 5.7 - Prob. 19ECh. 5.7 - Prob. 20ECh. 5.7 - Prob. 21ECh. 5.7 - Prob. 22ECh. 5.7 - Prob. 23ECh. 5.7 - Prob. 24ECh. 5.7 - Prob. 25ECh. 5.7 - Prob. 26PSCh. 5.7 - Prob. 27PSCh. 5.7 - Prob. 28PSCh. 5.7 - Prob. 29PSCh. 5.7 - Prob. 30PSCh. 5.7 - Prob. 31PSCh. 5.7 - Prob. 32PSCh. 5.7 - Prob. 1QCh. 5.7 - Prob. 2QCh. 5.7 - Prob. 3QCh. 5.7 - Prob. 4QCh. 5.7 - Prob. 5QCh. 5.7 - Prob. 1MRPSCh. 5.7 - Prob. 2MRPSCh. 5.7 - Prob. 3MRPSCh. 5.7 - Prob. 4MRPSCh. 5.7 - Prob. 5MRPSCh. 5.7 - Prob. 6MRPSCh. 5.7 - Prob. 7MRPSCh. 5 - Prob. 1VECh. 5 - Prob. 2VECh. 5 - Prob. 3VECh. 5 - Prob. 4VECh. 5 - Prob. 5VECh. 5 - Prob. 6REAECh. 5 - Prob. 7REAECh. 5 - Prob. 8REAECh. 5 - Prob. 9REAECh. 5 - Prob. 10REAECh. 5 - Prob. 11REAECh. 5 - Prob. 12REAECh. 5 - Prob. 13REAECh. 5 - Prob. 14REAECh. 5 - Prob. 15REAECh. 5 - Prob. 16REAECh. 5 - Prob. 17REAECh. 5 - Prob. 18REAECh. 5 - Prob. 19REAECh. 5 - Prob. 20REAECh. 5 - Prob. 21REAECh. 5 - Prob. 22REAECh. 5 - Prob. 23REAECh. 5 - Prob. 24REAECh. 5 - Prob. 25REAECh. 5 - Prob. 26REAECh. 5 - 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