Problem 57 - Algebra 1: Concepts and Skills

Question

Count the number of cubic units along the edges of the cube. Write and evaluate the power that gives the volume of the cube in cubic units.

Step-by-Step Solution

Answer

The volume of the cube can be calculated by cubing the length of any of its sides which can easily be counted by the number of cubic units along any edge of the cube.

Step 1: Understand the Problem

A cube has three dimensions: length, breadth, and height. In a cube, all these three dimensions are equal. Therefore, if we measure one side of the cube (in units), we will know the length of all sides.

Step 2: Count the cubic units

The number of cubic units along the edges of the cube is the same as the length of the edge. In other words, if we count the number of cubic units along an edge, we are essentially calculating the length of a side of the cube.

Step 3: Calculate the Volume

Once we have the length of a side (say \( n \)) in units, we can calculate the volume of the cube. The volume (V) of a cube is given by the formula \( V = n^3 \). Cube the value obtained in Step 2.

Step 4: Evaluate

Evaluate the cube of the value obtained in Step 2 to get the volume in cubic units.