Find the missing numbers for the dimensions and measures of a rectangular prism...
Length ?
Width 7 m
Height 5 m
Surface Area 214 m to the second power Volume ?
Please answer the one's with a ?. Thank you.
As = 2W*h + 2L*W + 2L*h = 214 m^2.
70 + 14L + 10L = 214
24L = 144
L = 6 m.
V = L*W*h = 6 * 7 * 5 = 210 m^3.
To find the missing dimensions and measures of a rectangular prism, we can use the given information about the width, height, surface area, and volume.
1. Width: The width is given as 7 meters.
2. Surface Area: The formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Given that the surface area is 214 m², we can substitute the known values and solve for the missing dimensions:
214 = 2(l)(7) + 2(l)(5) + 2(7)(5)
214 = 14l + 10l + 70
214 = 24l + 70
144 = 24l
l = 144/24
l = 6 m
So, the missing length is 6 meters.
3. Volume: The formula for the volume of a rectangular prism is V = lwh. We can substitute the known values to find the missing dimension:
V = (6)(7)(5)
V = 210 m³
Therefore, the missing volume is 210 cubic meters.
To summarize:
- Length: 6 m
- Width: 7 m
- Height: 5 m
- Surface Area: 214 m²
- Volume: 210 m³