   Chapter 9.1, Problem 33E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

When the length of each edge of a cube is increased by 1 cm, the volume is increase by 61 c m 3 . What is the length of each edge of the original cube?

To determine

To find:

The length of each edge of the original cube.

Explanation

The volume of any solid is the region of space occupied by it and in general the volume of a solid is given by the product of its base area and altitude.

For a regular solid prism with base area B and altitude h, the volume is given by the formula

V=Bh.

Calculation:

Given,

The edge of the original cube is ‘e’.

Each of the edge is increased by 1 cm to get a new cube and the volume is increased by 61 cm3.

First the volume of the original cube is given by the part ‘c’ of exercise 31 is

V=e3

Now, the volume of the new cube, obtained is given by replacing V as (V+61) cm3, as the volume is increased by 61 cm3 and ‘e’ by (e+1) cm as the edge is increased by 1 cm each.

Thus,

V+61=e+13

But, V=e3

e3+6=e+13

e3+61=e3+3e2+3e+1

Add; -e3 on both side,

e3+61+-e3=e3+3e2+3e+1+-e3

By the associative property of addition,

(e3-e3)+61=e3-e3+(3e2+3e+1)

61=3e2+3e+1

Add; -61 on both side,

61+-61=3

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Evaluate the integral. 1/21/241x2dx

Single Variable Calculus: Early Transcendentals, Volume I

In Problems 25-38, find y'. 26.

Mathematical Applications for the Management, Life, and Social Sciences

let f(x) = x 1, g(x) = x+1, and h(x) = 2x3 1. Find the rule for each function. 9. f + g

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

A population of N = 7 scores has a mean of = 13. What is the value of X for this population?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 110, evaluate the expression. 15!

Finite Mathematics for the Managerial, Life, and Social Sciences 