The volume of a rectangular prism is 1,000 cubic millimeters. Use the formula V equals l w hto determine which statements are true. Choose all that apply.
none applies
To determine which statements are true, we need to use the formula for the volume of a rectangular prism, which is given as V = lwh.
The volume of the rectangular prism is 1,000 cubic millimeters. The formula V = lwh tells us that the volume is obtained by multiplying the length, width, and height of the prism.
To find the possible combinations of length, width, and height that result in a volume of 1,000 cubic millimeters, we can start by listing all the factors of 1,000. The factors of 1,000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1,000.
We can then consider various combinations of these factors. For example, if we take the length as 10, width as 10, and height as 10, the product (10 × 10 × 10) is equal to 1,000, i.e., the desired volume. Hence, a possible combination is l = 10, w = 10, and h = 10.
Similarly, other combinations can be considered, such as l = 5, w = 10, and h = 20, or l = 2, w = 20, and h = 25, etc., resulting in the volume of 1,000.
Therefore, the statements that are true based on the given information are:
1. The length, width, and height can be integers.
2. The length, width, and height can be different.
3. The length, width, and height can be equal.