a rengular prism is made of 1-centimeter cubes. the volume of the rectangular prism i 60 cubic centimeters. which set of dimensionscould describe the rectangular prism?
Height * width * length = Volume
60 factors into 2 * 2 * 3 * 5. Use those to combine for the three dimensions.
5 * 6 * 2 = 60
5 * 3 * 4 = 60
To find the set of dimensions for the rectangular prism, we need to consider the volume of the prism.
The volume of a rectangular prism can be calculated by multiplying the length, width, and height of the prism.
Let's consider the factors of 60.
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
These factors represent all the possible values for the length, width, and height of the rectangular prism.
Here are some possible sets of dimensions that could describe the rectangular prism with a volume of 60 cubic centimeters:
1. Length = 3 cm, Width = 4 cm, Height = 5 cm
(3 cm x 4 cm x 5 cm = 60 cm³)
2. Length = 2 cm, Width = 6 cm, Height = 5 cm
(2 cm x 6 cm x 5 cm = 60 cm³)
3. Length = 6 cm, Width = 2 cm, Height = 5 cm
(6 cm x 2 cm x 5 cm = 60 cm³)
4. Length = 5 cm, Width = 3 cm, Height = 4 cm
(5 cm x 3 cm x 4 cm = 60 cm³)
Please note that there could be more sets of dimensions that could describe the rectangular prism, but these are some examples based on the given information.
To find the dimensions of the rectangular prism, we can divide the volume (60 cubic centimeters) by the total number of 1-centimeter cubes used.
Let's assume the dimensions of the rectangular prism are length (L), width (W), and height (H), all in centimeters. The volume (V) of a rectangular prism is calculated by multiplying its dimensions: V = L x W x H.
In this case, the volume is given as 60 cubic centimeters. We want to find the possible sets of dimensions. We can start by finding the factors of 60, as they can represent the possible combinations of the length, width, and height.
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Now, let's see which combinations of the factors would provide a volume of 60 cubic centimeters.
If we assign one factor to the length, another to the width, and the remaining one to the height, we can check if the volume matches our requirement. Let's go through the combinations:
1. L = 1, W = 2, H = 30, because (1 x 2 x 30) = 60. This is a valid combination.
2. L = 2, W = 3, H = 10, because (2 x 3 x 10) = 60. This is a valid combination.
3. L = 3, W = 4, H = 5, because (3 x 4 x 5) = 60. This is a valid combination.
4. L = 4, W = 5, H = 3, because (4 x 5 x 3) = 60. This is a valid combination.
5. L = 5, W = 6, H = 2, because (5 x 6 x 2) = 60. This is a valid combination.
6. L = 6, W = 10, H = 1, because (6 x 10 x 1) = 60. This is a valid combination.
7. L = 10, W = 6, H = 1, because (10 x 6 x 1) = 60. This is a valid combination.
8. L = 12, W = 5, H = 1, because (12 x 5 x 1) = 60. This is a valid combination.
9. L = 15, W = 4, H = 1, because (15 x 4 x 1) = 60. This is a valid combination.
10. L = 20, W = 3, H = 1, because (20 x 3 x 1) = 60. This is a valid combination.
11. L = 30, W = 2, H = 1, because (30 x 2 x 1) = 60. This is a valid combination.
12. L = 60, W = 1, H = 1, because (60 x 1 x 1) = 60. This is a valid combination.
Therefore, these are the sets of dimensions that could describe the rectangular prism:
- 1 cm x 2 cm x 30 cm
- 2 cm x 3 cm x 10 cm
- 3 cm x 4 cm x 5 cm
- 4 cm x 5 cm x 3 cm
- 5 cm x 6 cm x 2 cm
- 6 cm x 10 cm x 1 cm
- 10 cm x 6 cm x 1 cm
- 12 cm x 5 cm x 1 cm
- 15 cm x 4 cm x 1 cm
- 20 cm x 3 cm x 1 cm
- 30 cm x 2 cm x 1 cm
- 60 cm x 1 cm x 1 cm
8*8*15
=1.152in3.