Pre-Algebra
Pre-Algebra
1st Edition
ISBN: 9780618800766
Author: Ron Larson, Lee Stiff, Laurie Boswell, Timothy Kanold
Publisher: Houghton Mifflin-High School
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Chapter 10.6, Problem 29E

a.

To determine

To calculate the surface area of pyramid.

a.

Expert Solution
Check Mark

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

b.

To determine

To calculate the surface area of cone.

b.

Expert Solution
Check Mark

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

c.

To determine

To compare pyramid or cone have the greater area .

c.

Expert Solution
Check Mark

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

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Chapter 10.6, Problem 28E
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Chapter 10.6, Problem 31E

Chapter 10 Solutions

Pre-Algebra

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