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 41E

To determine

To find if the surface area of the first pyramid is one third of the surface area of the second pyramid.

Expert Solution & Answer

Answer to Problem 41E

The surface area of pyramid 2 is greater than pyramid 1, but not by 3 times.

Explanation of Solution

Given information:

Two pyramids have congruent bases.

The slant height of the first pyramid is one-third of the slant height of the second pyramid.

Formula used:

Surface area of pyramid,

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 1

Let l=x , where l is slant lenght

where s is square base side

where B is the base area where P is perimeter of base

For pyramid 1:

Assuming pyramid is square, Base area B and perimeter P will be,

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 2

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 3

Substituting value of B and P in surface area formula,

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 4

On solving,

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 5 .........(1)

For pyramid 2:

Assuming pyramid is square, Base area B and perimeter P will be,

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 6

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 7

Here, slant lenght is l=3x given in question.

Substituting value of B , P and l in surface area formula,

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 8

On solving,

Holt Mcdougal Larson Pre-algebra: Student Edition 2012, Chapter 10.6, Problem 41E , additional homework tip 9 .......(2)

On comparing equation (1)and(2),

SA of pyramid 2 is greater than SA of pyramid 1,but not 3 times.

Chapter 10.6, Problem 40E

Chapter 10.7, Problem 1C

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

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