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To determine how many rectangular prisms can be formed from 12 unit cubes, we must consider the possible dimensions (length, width, height) that multiply to 12. The factors of 12 give us several combinations, such as 1x1x12, 1x2x6, 1x3x4, and 2x2x3. Therefore, there are multiple distinct rectangular prisms that can be created using 12 unit cubes, depending on how we group the cubes into different dimensions.
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To determine how many different prisms can be made using 16 cm cubes, we first need to consider the dimensions of the prisms formed by combining these cubes. A prism's volume is calculated by multiplying the area of its base by its height, and since each cube has a volume of 1 cm³, the total volume of the prism will be 16 cm³. The different combinations of base dimensions (length, width, height) that multiply to 16 will yield various prism shapes, but the exact number of distinct prisms depends on the specific combinations of whole number dimensions that satisfy this condition, which can be calculated, but typically results in a limited number of unique configurations.
To determine how many different rectangular prisms can be made using 4 unit cubes, we can consider the possible dimensions that multiply to 4. The combinations of dimensions (length, width, height) are (1, 1, 4), (1, 2, 2), and (2, 1, 2). Since the order of dimensions matters, we need to account for permutations, resulting in three unique rectangular prisms: one with dimensions 1x1x4, and one with dimensions 1x2x2 (which accounts for two arrangements). Therefore, there are a total of 3 different rectangular prisms.
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Well, honey, if the height is 4 cubes, that leaves you with 12 cubes to work with for the base. You can arrange those 12 cubes in various ways to form different rectangular prisms. So, technically speaking, there are multiple rectangular prisms you can create with 48 cubes and a height of 4 cubes.
They are all called cuboids or hexahedra. There are no names that give more details about the prisms' structure.
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To determine how many rectangular prisms can be formed from 12 unit cubes, we must consider the possible dimensions (length, width, height) that multiply to 12. The factors of 12 give us several combinations, such as 1x1x12, 1x2x6, 1x3x4, and 2x2x3. Therefore, there are multiple distinct rectangular prisms that can be created using 12 unit cubes, depending on how we group the cubes into different dimensions.
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To determine how many different prisms can be made using 16 cm cubes, we first need to consider the dimensions of the prisms formed by combining these cubes. A prism's volume is calculated by multiplying the area of its base by its height, and since each cube has a volume of 1 cm³, the total volume of the prism will be 16 cm³. The different combinations of base dimensions (length, width, height) that multiply to 16 will yield various prism shapes, but the exact number of distinct prisms depends on the specific combinations of whole number dimensions that satisfy this condition, which can be calculated, but typically results in a limited number of unique configurations.
To determine how many different rectangular prisms can be made using 4 unit cubes, we can consider the possible dimensions that multiply to 4. The combinations of dimensions (length, width, height) are (1, 1, 4), (1, 2, 2), and (2, 1, 2). Since the order of dimensions matters, we need to account for permutations, resulting in three unique rectangular prisms: one with dimensions 1x1x4, and one with dimensions 1x2x2 (which accounts for two arrangements). Therefore, there are a total of 3 different rectangular prisms.
You can create five distinct rectangular prisms using 6 unit cubes. The possible dimensions are 1x1x6, 1x2x3, and their permutations, leading to the following combinations: 1x1x6, 1x2x3, and 2x3x1. Each combination can be arranged in different orientations, but the unique shapes remain limited to these configurations.
To find the number of different rectangular prisms that can be built using 18 unit cubes, we need to determine the possible dimensions ( (l, w, h) ) such that ( l \times w \times h = 18 ), where ( l ), ( w ), and ( h ) are positive integers. The factor combinations of 18 are: ( (1, 1, 18) ), ( (1, 2, 9) ), ( (1, 3, 6) ), ( (2, 3, 3) ), and their permutations. Counting unique arrangements, there are a total of 6 distinct rectangular prisms that can be formed.
To determine the number of rectangular prisms that can be formed using exactly 36 cubes, we need to find all the possible combinations of dimensions that can multiply to give 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Each factor corresponds to a unique rectangular prism. Therefore, there are 9 different rectangular prisms that can be formed using exactly 36 cubes.