   Chapter 9.1, Problem 35E ### 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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# The sum of the lengths of all edges of a cube is 60 cm. Find the volume V and the surface area T of the cube.

To determine

To find:

The volume V and the surface area T of the cube such that the sum of the lengths of all edges of the cube is 60 cm.

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.

The lateral area of any solid is the area of all the number of lateral sides that it have, excluding the area of the top and the bottom of the solid.

The lateral area (L) of any solid prison with the perimeter of the base of the prism as (P) and altitude ‘h’ is given by the formula

L=Ph.

Here, P is the perimeter of any one of the base of the prism and which is given by the sum of all the sides of the base.

Calculation:

Given,

The sum or the length of all edges of the cube is 60 cm.

Let ‘x’ be the length of each side of the cube.

A cube has 4 lateral edges and 8 base edges, in total it has 12 edges.

Since, each edge measures of length ‘x’,

We have;

12x=60

12x12=6012

x=5

Thus, the length of each edge of the cube is 5 cm

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