To find the number of rectangular prisms with a volume of 36 cm³, we need to determine the integer factor combinations of 36. The volume of a rectangular prism is given by the formula ( V = l \times w \times h ), where ( l ), ( w ), and ( h ) are the length, width, and height, respectively. The positive integer factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. By considering all combinations of these factors that satisfy the equation ( l \times w \times h = 36 ), we find there are 10 distinct rectangular prisms.
4
9
4
To find the number of rectangular prisms with a volume of 24 using 24 cubes, you need to determine the possible dimensions (length, width, height) that multiply to 24. The possible factor combinations of 24 that represent the dimensions of a rectangular prism are (1, 1, 24), (1, 2, 12), (1, 3, 8), (1, 4, 6), (2, 2, 6), and (2, 3, 4). However, each combination can be arranged in different ways, so considering unique arrangements, you can make a total of 10 distinct rectangular prisms.
1 regetangular prism
4
9
There are 4 of them.
4
Four.
1 regetangular prism
Three.
To determine how many rectangular prisms can be made from 140 cubes, we need to consider the volume of the prisms, which is given by the formula ( V = l \times w \times h ) (length × width × height). The task involves finding all combinations of positive integers ( l ), ( w ), and ( h ) such that their product equals 140. The number of distinct rectangular prisms is equal to the number of unique factorizations of 140 into three positive integers, which can vary based on the order of dimensions.
You can do it ten times, I had an assignment and we had to make ten rectangular prisms 10 times
An infinite amount. If you only want to count integral lengths, then there's only one: 1 by 1 by 11. (This is because 11 is a prime number.)
There are only four different configurations.
A cube or cuboid.