fill in the missing values for a retangular prism.
length__________?
width 7
height 5
surface area 358
volume __________?
Formula
SA = 2(LxW) + 2(LxH) + 2(WxH)
First insert values in above equation to calculate L.
Then use values to calculate Volume = L * H * W
(Online "*" is used to indicate multiplication, because "x" is often confused with an unknown.)
165
To solve for the missing values, we can use the given formula for surface area:
SA = 2(L x W) + 2(L x H) + 2(W x H)
Given:
Width (W) = 7
Height (H) = 5
Surface Area (SA) = 358
We can substitute these values into the formula and solve for the missing values.
358 = 2(L x 7) + 2(L x 5) + 2(7 x 5)
To simplify, we can distribute the multiplication:
358 = 14L + 10L + 70
Combine like terms:
358 = 24L + 70
Subtract 70 from both sides:
288 = 24L
Divide both sides by 24:
L = 12
So, the missing value for length is 12.
Now, to calculate the volume, we can use the formula for volume of a rectangular prism:
Volume = L x W x H
Substituting the values:
Volume = 12 x 7 x 5
Volume = 420
So, the missing value for volume is 420.