fill in the missing vvalues for a retangular prism.
length__________?
width 7
height 5
surface area 358
volume __________?
sa = 2(lw) + 2(lh) + 2(wh)
To fill in the missing values for a rectangular prism, we can use the formula for surface area:
Surface Area (SA) = 2(length x width) + 2(length x height) + 2(width x height)
Given values:
Width = 7
Height = 5
Surface Area (SA) = 358
Now let's solve for the missing values.
Step 1: Calculate the surface area of the rectangular prism.
Since we know the surface area (SA) is 358, we can substitute the given values into the formula to solve for length (l):
358 = 2(l x 7) + 2(l x 5) + 2(7 x 5)
Simplifying the equation:
358 = 14l + 10l + 70
Combining like terms:
358 = 24l + 70
Subtracting 70 from both sides of the equation:
288 = 24l
Dividing both sides of the equation by 24:
l = 12
Therefore, the missing length value for the rectangular prism is 12.
Step 2: Calculate the volume of the rectangular prism.
To find the volume (V), we can use the formula:
Volume (V) = length x width x height
Substituting the known values into the volume formula:
V = 12 x 7 x 5
Multiplying:
V = 420
Therefore, the missing volume value for the rectangular prism is 420.