Fill in missing values for a rectangular prism? Length is 8. Width is missing. Height is 14. Surface area is missing. Volume is 324.8
V = lwh
324.8 = 8 * 14 * W
324.8 = 112W
2.9 = W
To fill in the missing values for the rectangular prism, we can use the formulas for surface area and volume.
The formula for the surface area of a rectangular prism is:
Surface Area = 2 * (Length * Width + Length * Height + Width * Height)
Given that the length is 8, the height is 14, and the surface area is missing, we can substitute these values into the formula and solve for the missing width:
Surface Area = 2 * (8 * Width + 8 * 14 + Width * 14)
Since the surface area is missing, we can set it equal to x (unknown value):
x = 2 * (8 * Width + 8 * 14 + Width * 14)
Next, let's solve for the missing width by isolating it in the equation:
x = 2 * (8 * Width + 112 + 14 * Width)
x = 16 * Width + 224 + 28 * Width
x = 44 * Width + 224
Since the width is still missing, we cannot solve for it yet. We will need more information or another equation.
Moving on to the volume, the formula for the volume of a rectangular prism is:
Volume = Length * Width * Height
Given that the length is 8, the height is 14, and the volume is 324.8, we can substitute these values into the formula:
324.8 = 8 * Width * 14
Now, let's solve for the missing width by isolating it in the equation:
324.8 = 112 * Width
Width = 324.8 / 112
Width ≈ 2.9
Therefore, the missing width of the rectangular prism is approximately 2.9 units.
To fill in the missing values for a rectangular prism, we can use the formulas for surface area and volume.
1. Length: Given as 8 units.
2. Width: This value is missing. To find it, we need to rearrange the formula for volume and substitute in the given values. The formula for volume of a rectangular prism is V = Length * Width * Height. Knowing that the volume is 324.8 and the length and height are given, we can rearrange the formula as Width = V / (Length * Height). Plugging in the values, we get Width = 324.8 / (8 * 14). Calculating this gives Width ≈ 3.6786 units.
3. Height: Given as 14 units.
4. Surface Area: This value is missing. To find it, we can use the formula for surface area of a rectangular prism, which is A = 2 * (Length * Width + Length * Height + Width * Height). For this calculation, we need the values of length, width, and height. Plugging in the known values, we get A = 2 * (8 * 3.6786 + 8 * 14 + 3.6786 * 14). Calculating this gives Surface Area ≈ 404.7712 square units.
So, the missing values in the rectangular prism are: Width ≈ 3.6786 units and Surface Area ≈ 404.7712 square units.