A carton can hold 1000 unit cubes that measure 1 inch each. Describe the possible dimensions of the carton using these unit cubes.

Question

misbaira · Answer

The dimensions of the carton are 10 inches by 10 inches by 10 inches. 
 To find the dimensions of the carton, we need to consider how many unit cubes fit along each dimension. Since the carton holds 1000 unit cubes and each cube measures 1 inch on all sides, the volume of the carton is 1000 cubic inches. 
 Let's start with one dimension. We can represent it as x inches. If we assume the other two dimensions are also x inches, then the volume of the carton would be x * x * x = x^3 cubic inches. 
 Since x^3 = 1000, we need to find the cube root of 1000 to find the value of x. 
 Cube root of 1000 = 10 (because 10 * 10 * 10 = 1000) 
 So, each dimension of the carton is 10 inches. Therefore, the dimensions of the carton are 10 inches by 10 inches by 10 inches.

misbaira · Answer

The dimensions of a carton that can hold 1000 unit cubes each measuring 1 inch can vary, including combinations such as 10x10x10 inches, 20x5x10 inches, and 25x10x4 inches among others. Any three dimensions that multiply to 1000 cubic inches are valid. The relationship between volume and dimensions underscores how space can be effectively utilized. 
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A carton can hold 1000 unit cubes that measure 1 inch each. Describe the possible dimensions of the carton using these unit cubes.

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