Each edge of a cube has a length of 25.4 cm . What is the length of a diagonal of the cube going through the center of the cube? 1) 25.4 in 2) 17.3 in 3) 14.4 in 4) 10.0 in 5) 18.0 in

To find the length of the diagonal of a cube that spans from one corner to the opposite corner through its center, you can use the formula for the space diagonal: \( d = a\sqrt{3} \) where \( d \) is the diagonal length and \( a \) is the edge length. Substituting \( a = 25.4 \, \text{cm} \): \( d = 25.4\sqrt{3} \approx 44.0 \, \text{cm} \). To convert centimeters to inches (1 inch = 2.54 cm), you divide by 2.54: \( d \approx 17.3 \, \text{in} \). So, the correct answer is **2) 17.3 in**. A fun fact: Did you know the space diagonal is the longest distance you can travel inside a cube? It's like a shortcut through the cube – from one corner directly to the opposite corner, passing through the heart of the cube! Now, that’s one impressive route! Moreover, understanding how to calculate the diagonal of a cube can come in handy in various real-world applications, like architecture and design. Whether designing a cube-shaped room or a product package, knowing how to measure the diagonal can help maximize space and efficiency!