The volume of a rectangular prism is 1,000 mm cubed. Use the formula V=lwh to determine which statements are true. Choose all that apply
The prism could be a cube with a side length of 10mm *
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
almost.
C is wrong (see your answer to B)
1000 = 25*40 = 2.5 * 400
So, only C must be false
A rectangular prism is 1 millimeter long and 8 millimeters wide. Its volume is 40 cubic millimeters. What is the height of the rectangular prism?
The statements that are true are:
- The prism could be a cube with a side length of 10mm.
- It is possible for the length to be 1,000 mm.
To determine which statements are true, let's analyze the formula for the volume of a rectangular prism: V = lwh, where l represents the length, w represents the width, and h represents the height.
Statement 1: "The prism could be a cube with a side length of 10mm."
To check if this statement is true, let's substitute the values into the formula: V = lwh. If V = 1,000 mm³ and we assume l = w = h = 10 mm, the equation becomes 1,000 = 10 * 10 * 10 = 10,000, which is not correct. Therefore, statement 1 is false.
Statement 2: "It is possible for the length to be 1,000 mm."
To check if this statement is true, we can again use the formula. If V = 1,000 mm³ and we assume w = 1 mm and h = 1,000 mm, we can rearrange the formula to solve for l: l = V / (wh) = 1,000 / (1 * 1,000) = 1. So, it is possible for the length to be 1,000 mm, and statement 2 is true.
Statement 3: "The length, width, and height must end in zero."
According to the formula V = lwh, there is no requirement for the length, width, or height to end in zero. For example, if we assume l = 4 mm, w = 5 mm, and h = 50 mm, the product (4 * 5 * 50) equals 1,000 mm³. Therefore, statement 3 is false.
Statement 4: "It is possible that the length is 2.5 mm."
To check if this statement is true, we can once again use the formula. If V = 1,000 mm³ and we assume w = 2.5 mm and h = 160 mm, we can rearrange the formula to solve for l: l = V / (wh) = 1,000 / (2.5 * 160) ≈ 2. If the length can be approximately 2 mm, then it is possible for the length to be 2.5 mm. Therefore, statement 4 is true.
In summary, statement 2 ("It is possible for the length to be 1,000 mm") and statement 4 ("It is possible that the length is 2.5 mm") are true, while statement 1 ("The prism could be a cube with a side length of 10mm") and statement 3 ("The length, width, and height must end in zero") are false.