Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN: 9780547587776

Author: HOLT MCDOUGAL

Publisher: HOLT MCDOUGAL

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Question

Chapter 10.6, Problem 29E

To determine

To calculate the surface area of pyramid.

Expert Solution

Answer to Problem 29E

144 ft.2

Explanation of Solution

Given Information: Pyramid Base b = 8 ft., Radius r=Base b2 = 82 = 4 ft. and Height h = 3 ft.

Formula Used:

Surface area of square pyramid = 2(b×s) + b2 , Slant Height s= h2+r2

Calculation:

Surface area of square pyramid = 2(b×s) + b2

Now, find Slant Height s.

Slant Height of Pyramid s= h2+r2

Radius r = 4 ft., Height h = 3 ft.

Now put the value of r and h to find Slant Height of Pyramid

Slant Height of Pyramid s= 32+42 ft.

So,

Slant Height of Pyramid s= 9+ 16 ft.

So,

Slant Height of Pyramid s= 25 ft.

Hence,

Slant Height of Pyramid s=5 ft.

Surface area of square pyramid = 2(b×s) + b2

Base b = 8 ft. and Slant Height s = 5 ft.

Now put the value of b and s to find Surface area of square pyramid

Surface area of square pyramid = 2(8×5) + 82 ft.2

So,

Surface area of square pyramid = 2×(40) + 64 ft.2

So,

Surface area of square pyramid = 80 + 64 ft.2

Hence,

Surface area of square pyramid = 144 ft.2

To determine

To calculate the surface area of cone.

Expert Solution

Answer to Problem 29E

113.14 ft²

Explanation of Solution

Given Information: Cone Diameter d = 8 ft., Height h = 3 ft. and π=227

Formula Used:

Surface area of Cone = πr2+ πrl , Radius = Diameter2 , Slant Height of Cone s= h2+r2

Calculation:

Surface area of Cone = πr2+ πrl

Diameter d = 8 ft., Height h = 3 ft. and π=227

First find Radius r.

Hence,

Radius = Diameter2

Put the value of diameter to find radius of Cone

Radius = 82

So,

Radius r = 4 ft.

Now, find Slant Height s.

Slant Height of Cone s= h2+r2

Radius r = 4 ft., Height h = 3 ft.

Now put the value of r and h to find Slant Height of Cone

Slant Height of Cone s= 32+42 ft.

So,

Slant Height of Cone s= 9+ 16 ft.

So,

Slant Height of Cone s= 25 ft.

Hence,

Slant Height of Cone s=5 ft.

Surface area of Cone = πr2+ πrl

Radius r = 4 ft., Slant Height s = 5 ft.

Now put the value of r, s and π to find Surface area of Cone

Surface area of Cone = 227×42 + 227×4×5 ft²

So,

Surface area of Cone = 227×16 + 227×20 ft²

So,

Surface area of Cone = 227×(16 + 20) ft²

So,

Surface area of Cone = 227×36 ft²

Hence,

Surface area of Cone = 113.14 ft²

To determine

To compare pyramid or cone have the greater area .

Expert Solution

Answer to Problem 29E

Surface area of square pyramid is greater than Surface area of Cone.

Explanation of Solution

Given Information:

Surface area of square pyramid = 144 ft.2

Surface area of Cone = 113.14 ft²

Formula Used:Comparison

Calculation:

As Checked,

Surface area of square pyramid = 144 ft.2

Surface area of Cone = 113.14 ft²

Surface area of square pyramid is greater than Surface area of Cone.

144 ft²>113.14 ft²

Chapter 10.6, Problem 28E

Chapter 10.6, Problem 31E

Chapter 10 Solutions

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

Ch. 10.1 - Prob. 1C Ch. 10.1 - Prob. 2C Ch. 10.1 - Prob. 3C Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E

Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.2 - Prob. 1C Ch. 10.2 - Prob. 2C Ch. 10.2 - Prob. 3C Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - 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