how do you find possible dimension of a rectangular prism that has a volume of 320 in3
set up a proportion
320 in^3 = 320 cubic inches
Factor 320 into three factors.
8 * 4 * 10?
8 * 8 * 5?
2 * 16 * 10?
To find the possible dimensions of a rectangular prism with a volume of 320 in³, we need to determine the combinations of length, width, and height that can give us the desired volume.
The volume of a rectangular prism, V, is given by the formula V = length × width × height.
In this case, we have V = 320 in³. So, we need to find three positive integers (length, width, and height) whose product equals 320. To do this, we can factorize 320 and consider all possible combinations.
Let's start by finding the prime factorization of 320:
320 = 2 × 2 × 2 × 2 × 2 × 2 × 5
Now, let's consider the different combinations of these factors to find the possible dimensions:
Combination 1: 2 × 2 × 2 × 2 × 2 × 2 × 5
Here, we have length = 2, width = 2, and height = 2 × 2 × 2 × 5 = 40. So, one possible dimension is 2 in by 2 in by 40 in.
Combination 2: 4 × 2 × 2 × 2 × 5
Here, we have length = 4, width = 2, and height = 2 × 2 × 5 = 20. So, another possible dimension is 4 in by 2 in by 20 in.
Combination 3: 4 × 4 × 2 × 5
Here, we have length = 4, width = 4, and height = 2 × 5 = 10. So, another possible dimension is 4 in by 4 in by 10 in.
Combination 4: 8 × 2 × 2 × 5
Here, we have length = 8, width = 2, and height = 2 × 5 = 10. So, another possible dimension is 8 in by 2 in by 10 in.
Combination 5: 8 × 2 × 5 × 2
Here, we have length = 8, width = 2, and height = 5 × 2 = 10. So, another possible dimension is 8 in by 2 in by 10 in.
Combination 6: 8 × 4 × 5
Here, we have length = 8, width = 4, and height = 5. So, another possible dimension is 8 in by 4 in by 5 in.
Combination 7: 16 × 2 × 5
Here, we have length = 16, width = 2, and height = 5. So, another possible dimension is 16 in by 2 in by 5 in.
Combination 8: 16 × 4 × 2
Here, we have length = 16, width = 4, and height = 2. So, another possible dimension is 16 in by 4 in by 2 in.
Therefore, the possible dimensions of the rectangular prism with a volume of 320 in³ are:
- 2 in by 2 in by 40 in
- 4 in by 2 in by 20 in
- 4 in by 4 in by 10 in
- 8 in by 2 in by 10 in
- 8 in by 2 in by 10 in
- 8 in by 4 in by 5 in
- 16 in by 2 in by 5 in
- 16 in by 4 in by 2 in