Chapter 9.1, Problem 33E

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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

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

**Calculation:**

Given,

The edge of the original cube is â€˜

Each of the edge is increased by 1 cm to get a new cube and the volume is increased by 61 cm^{3}.

First the volume of the original cube is given by the part â€˜

Now, the volume of the new cube, obtained is given by replacing ^{3}, as the volume is increased by 61 cm^{3} and â€˜

Thus,

But,

Add;

By the associative property of addition,

Add;

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