A rectangular prism has a volume of 1,728 cubic units. The length is twice the width, and the height is 3 times the width. Find the width.

Mon, 04 May 2026 16:39:07 +0000

**A rectangular prism has a volume of 1,728 cubic units. The length is twice the width, and the height is 3 times the width. Find the width.** Why are so many people turning their attention to the math behind everyday shapes like rectangular prisms lately? Curious minds are exploring how geometry connects with real-world applications—from shipping containers and furniture design to architecture and even product packaging. When a shape’s volume totals 1,728 cubic units, with its length twice its width and its height three times that same width, solving for the width unlocks more than just a number—it reveals how precise measurement shapes efficiency and innovation. This isn’t just a textbook problem; it’s a practical example of how integers and ratios work together to solve real design challenges, making it increasingly relevant in construction, manufacturing, and digital visualization tools used today. The formula for the volume of a rectangular prism is length times width times height. Given the relationships—length equals two times the width, height equals three times the width—you can substitute into the volume equation:
**Volume = (2w) × w × (3w)**
That simplifies neatly to:
**Volume = 6w³**
With a known volume of 1,728 cubic units, the equation becomes:
6w³ = 1,728 This is the key step that transforms curiosity into calculation. Solving for w³ means dividing both sides by 6:
w³ = 1,728 ÷ 6
w³ = 288