Find 3 possible sets of dimensions for a rectangular prism with volume 24 cm³. Which rectangular prism would require the least amount of material to construct?
Three possible sets of dimensions for a rectangular prism with volume 24 cm³ are:
- 2 cm x 3 cm x 4 cm
- 1 cm x 4 cm x 6 cm
- 1.5 cm x 2 cm x 8 cm
To find which rectangular prism would require the least amount of material to construct, we need to calculate the surface area of each prism. The surface area is the sum of the areas of all six faces of the rectangular prism.
For the first set of dimensions (2 cm x 3 cm x 4 cm):
- Surface area = 2(2x3 + 3x4 + 2x4) = 2(6+12+8) = 52 cm²
For the second set of dimensions (1 cm x 4 cm x 6 cm):
- Surface area = 2(1x4 + 4x6 + 1x6) = 2(4+24+6) = 68 cm²
For the third set of dimensions (1.5 cm x 2 cm x 8 cm):
- Surface area = 2(1.5x2 + 2x8 + 1.5x8) = 2(3+16+12) = 62 cm²
Therefore, the rectangular prism with dimensions 2 cm x 3 cm x 4 cm would require the least amount of material to construct as it has the smallest surface area.