The volume of a rectangular prism is 1,000^3 mm. Use the formula V = lwh to determine which of the statements are true. Choose all that apply
The prism could be a cube with a side length of 10 mm.***
It is possible for the length to be 1,000 mm.***
The length, width, and height must end in zero.
It is possible that the length is 2.5 mm.***
looks good
To determine which statements are true, let's substitute the given volume, V = 1,000^3 mm, into the formula for the volume of a rectangular prism, V = lwh.
1. The prism could be a cube with a side length of 10 mm.
By substituting the values into the formula, we have 1,000^3 = 10 * 10 * 10 = 1,000 mm^3.
Therefore, the statement is true.
2. It is possible for the length to be 1,000 mm.
By substituting the values into the formula, we have 1,000^3 = 1,000 * w * h.
Dividing both sides of the equation by 1,000, we get 1,000^2 = w * h.
Since the length, w, and h are both positive integers, the statement is true.
3. The length, width, and height must end in zero.
From the formula V = lwh and the given volume V = 1,000^3 mm, we can see that the length, width, and height do not necessarily have to end in zero. Therefore, the statement is false.
4. It is possible that the length is 2.5 mm.
Substituting the values into the formula, we have 1,000^3 = 2.5 * w * h. However, since the volume is expressed in cubic millimeters (mm^3), the length should also be in millimeters (mm). Thus, it is not possible for the length to be 2.5 mm. Therefore, the statement is false.
In summary, the true statements are:
- The prism could be a cube with a side length of 10 mm.
- It is possible for the length to be 1,000 mm