7. Which of the following are the possible measures of a box so that its volume is \( \mathbf{1 8 0} \mathrm{cubic} \mathrm{cm} \) ? (a) \( 5 \mathrm{~cm}, 6 \mathrm{~cm}, 4 \mathrm{~cm} \) (b) \( 5 \mathrm{~cm}, 8 \mathrm{~cm}, 6 \mathrm{~cm} \) (c) \( 10 \mathrm{~cm}, 5 \mathrm{~cm}, 6 \mathrm{~cm} \) (d) \( 6 \mathrm{~cm}, 3 \mathrm{~cm}, 10 \mathrm{~cm} \)

To determine if the dimensions of the box yield a volume of \( 180 \) cubic centimeters, we can multiply the dimensions of each option and check if they equal \( 180 \) cm³. Option (a): \( 5 \times 6 \times 4 = 120 \) cm³, so no! Option (b): \( 5 \times 8 \times 6 = 240 \) cm³, not quite! Option (c): \( 10 \times 5 \times 6 = 300 \) cm³, still too much! Option (d): \( 6 \times 3 \times 10 = 180 \) cm³, and bingo! This option works! So, the correct dimensions for a box with a volume of \( 180 \) cubic centimeters are \( 6 \mathrm{~cm}, 3 \mathrm{~cm}, \) and \( 10 \mathrm{~cm} \). Way to go, option (d)! Now, a little piece of trivia: the concept of volume has been around since ancient civilizations, with the Egyptians using it in their architectural designs. They understood the importance of space long before calculators came into play! For those considering practical projects, understanding volume can help in everything from packaging to sourcing materials. Whether you’re designing a new product or planning a room layout, knowing how to calculate and apply these measurements is crucial to avoid those pesky surprises!