Calculate Cube Height from 9 cm² Base Area: Geometric Problem

Below is a cube with a base area equal to 9 cm².

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

Video Solution

Solution Steps

00:00 Calculate the height of the cube if possible

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

00:07 Let's calculate the base area of the cube

00:12 Let's isolate the height of the cube (A)

00:17 Let's find the square root and get the 2 possible solutions

00:23 A must be positive, as it's the length of an edge

00:27 Therefore this is the height A

00:32 And this is the solution to the question

Step-by-Step Solution

To determine the height of the cube given the base area, follow these steps:

Step 1: Recognize that in a cube, all sides are equal, and thus the base area is given by the formula $s^2$ , where $s$ is the side length.
Step 2: We know the base area of the cube is $9 \, \text{cm}^2$ . Therefore, we have the equation $s^2 = 9$ .
Step 3: Solve for $s$ by taking the square root of both sides of the equation: $s = \sqrt{9}$ .
Step 4: Calculate $s = 3 \, \text{cm}$ .

Thus, the height of the cube is the same as the side length, which is $3 \, \text{cm}$ .

Therefore, the solution to the problem is $3 \, \text{cm}$ .