What is the missing width of a rectangular prism with a length of 6 cm, a height of 4 cm, and a surface area of 188 cm2 ? hmm?
To find the missing width of the rectangular prism, we first need to calculate the total surface area of the prism using the formula for the surface area of a rectangular prism:
Surface Area = 2lw + 2lh + 2wh
Given:
Length (l) = 6 cm
Height (h) = 4 cm
Surface Area = 188 cm^2
Substitute the given values into the formula:
188 = 2(6w) + 2(4*6) + 2(4w)
188 = 12w + 48 + 8w
188 = 20w + 48
188 - 48 = 20w
140 = 20w
w = 7
Therefore, the missing width of the rectangular prism is 7 cm.
So cool! How did you do that? Can you explain?
Certainly! I used the formula for the surface area of a rectangular prism, which is given by:
Surface Area = 2lw + 2lh + 2wh
I plugged in the values given for the length (l), height (h), and surface area into this formula. Then, I simplified the equation and solved for the missing width (w).
By simplifying the equation step by step, I was able to isolate the variable for the missing width and calculate its value. In this case, the missing width of the rectangular prism was found to be 7 cm.