The volume of a rectangular prism is 1000 mm3. Use the formula V = lwh to determine which statements are true choose all that apply
1. The length, width, and height could all be 10 mm.
2. The length, width, and height could all be 100 mm.
3. The length could be 10 mm, the width could be 20 mm, and the height could be 50 mm.
4. The length could be 5 mm, the width could be 20 mm, and the height could be 25 mm.
5. The length could be 10 mm, the width could be 40 mm, and the height could be 2.5 mm.
To check which statements are true, we can calculate the volume of the rectangular prism using the given values of length, width, and height, and see if it equals 1000 mm3.
1. V = lwh = 10 x 10 x 10 = 1000 mm3 (True)
2. V = lwh = 100 x 100 x 100 = 1,000,000 mm3 (False)
3. V = lwh = 10 x 20 x 50 = 10,000 mm3 (False)
4. V = lwh = 5 x 20 x 25 = 2500 mm3 (False)
5. V = lwh = 10 x 40 x 2.5 = 1000 mm3 (True)
Therefore, statements 1 and 5 are true.
To determine which statements are true, let's first analyze the formula for the volume of a rectangular prism:
V = lwh
where:
V represents the volume of the prism,
l represents the length,
w represents the width, and
h represents the height.
Given that the volume of the rectangular prism is 1000 mm³, we can now evaluate the statements:
1. If the length (l) is 10 mm, the width (w) is 10 mm, and the height (h) is 10 mm:
V = 10 mm * 10 mm * 10 mm = 1000 mm³
Therefore, this statement is true because the given values satisfy the volume equation.
2. If the length (l) is 20 mm, the width (w) is 10 mm, and the height (h) is 5 mm:
V = 20 mm * 10 mm * 5 mm = 1000 mm³
Therefore, this statement is also true since the values satisfy the volume equation.
3. If the length (l) is 40 mm, the width (w) is 10 mm, and the height (h) is 5 mm:
V = 40 mm * 10 mm * 5 mm = 2000 mm³
Consequently, this statement is false because the calculated volume does not match the given volume.
In summary, statements 1 and 2 are true.
To determine which statements are true regarding the volume of a rectangular prism, we can use the equation V = lwh, where V represents the volume, l represents the length, w represents the width, and h represents the height.
1. If the volume is 1000 mm^3, then it is necessary to know at least two of the dimensions (length, width, or height) to find the missing dimension.
2. If the length is 10 mm and the width is 20 mm, then the height must be 5 mm to have a volume of 1000 mm^3. (True)
3. If the length is 50 mm and the width is 10 mm, then the height must be 2 mm to have a volume of 1000 mm^3. (True)
4. If the length is 100 mm, the width is 5 mm, and the height is 2 mm, then the volume will not be 1000 mm^3. (False)
Therefore, the true statements are:
- If the length is 10 mm and the width is 20 mm, then the height must be 5 mm to have a volume of 1000 mm^3.
- If the length is 50 mm and the width is 10 mm, then the height must be 2 mm to have a volume of 1000 mm^3.