Calculate Cube Volume from 16 cm² Base Area: Step-by-Step Solution

Below is a cube with a base area of 16 cm².

Is it possible to calculate the volume of the cube? If so, then what is it?

Video Solution

Solution Steps

00:00 Calculate the volume of the cube if possible

00:03 In a cube all edges are equal, let's mark it as A

00:07 We'll use the formula to calculate the base area (edge squared)

00:10 We'll find the square root and get 2 possible solutions

00:15 A must be positive, as it's the length of an edge

00:19 This is the size of edge A

00:23 We'll use the formula to calculate volume (edge cubed)

00:30 We'll substitute the edge value we found and solve for volume

00:34 And this is the solution to the problem

Step-by-Step Solution

To determine if it is possible to calculate the volume of the cube and then find it, we proceed as follows:

Step 1: Identify the given information
The base area of the cube is given as $16 \, \text{cm}^2$ .
Step 2: Apply the appropriate formula for the side length
Since the base of a cube is a square, we have $s^2 = 16$ , where $s$ is the side length.
Step 3: Calculate the side length
Solving for $s$ , we find $s = \sqrt{16} = 4 \, \text{cm}$ .
Step 4: Calculate the volume of the cube
The volume $V$ of a cube with side $s$ is $V = s^3$ . Substituting in the side length, we get $V = 4^3 = 64 \, \text{cm}^3$ .

Therefore, it is possible to calculate the volume of the cube, and the volume is $64 \, \text{cm}^3$ .