A rectangular prism has dimensions of 3 cm by 4 cm by 5 cm. If the prism is scaled up by a factor of 3, what is the volume of the new prism?

Wed, 15 Apr 2026 22:52:01 +0000

A rectangular prism with dimensions 3 cm by 4 cm by 5 cm represents a fundamental shape studied across science, engineering, and design. Its simple proportions make it a go-to example when visualizing volume and scaling principles. For anyone interested in real-world applications, understanding how changing size impacts volume unlocks deeper insights into geometry’s role in everything from product manufacturing to architecture. When scaled up by a factor—like 3 times the original—calculations reveal not just a larger object, but a transformed space with predictable mathematical relationships. This scale-up process is key in industries where precision matters, such as packaging, construction, and product development. Narrowing into the math offers clarity in a world where visualizing scale can influence everything from shipping efficiency to space optimization—and that’s driving growing interest across the US market. This particular prism stands out because its original volume is fully calculable: 3 × 4 × 5 equals 60 cubic centimeters. Scaling every dimension uniformly by a factor of 3 doesn’t just increase length or width—it transforms volume dramatically. Volume depends on length, width, and height all scaled, creating a cubic increase. Instead of multiplying each dimension individually, there’s a smarter, faster method: multiply the original volume by the cube of the scale factor. Since 3³ equals 27, the new volume becomes 60 × 27 = 1,620 cubic centimeters—far more than a simple linear jump. This cubic growth reflects how three-dimensional space expands, a