   Chapter 9.1, Problem 33E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# 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

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

61+-61=3

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