Cube Measurements and Calculations
I see an image with text stating "cube edge = 5.4 cm," which suggests you're dealing with a cube whose edge length is 5.4 centimeters. However, the specific question or problem you need to solve concerning the cube is not visible in the image. Typically with cube-related problems, you might be asked to calculate the volume, surface area, or perhaps the diagonal of the cube. Here's how you would calculate each of these:
1. Volume of a Cube:
The volume \( V \) of a cube is calculated by cubing the length of one of its edges \( e \):
\[ V = e^3 \]
So for a cube with an edge of 5.4 cm,
\[ V = 5.4 \text{ cm} \times 5.4 \text{ cm} \times 5.4 \text{ cm} = 157.464 \text{ cm}^3 \]
2. Surface Area of a Cube:
The surface area \( A \) is calculated by multiplying the square of the edge length by six (since there are six sides on a cube):
\[ A = 6e^2 \]
Using the edge length 5.4 cm,
\[ A = 6 \times (5.4 \text{ cm})^2 = 6 \times 29.16 \text{ cm}^2 = 174.96 \text{ cm}^2 \]
3. Diagonal of a Cube:
The space diagonal \( d \) of a cube can be calculated using the formula, derived from the Pythagorean theorem in three dimensions:
\[ d = e\sqrt{3} \]
For an edge length of 5.4 cm,
\[ d = 5.4 \text{ cm} \times \sqrt{3} \approx 5.4 \text{ cm} \times 1.732 \approx 9.353 \text{ cm} \]
Without the specific question, I provided the formulas and calculations for typical cube measurements. If your question is about one of these measurements or something else related to the cube, please provide more details.
