Answer:
let's try the "Divide and Conquer" method, that is we break down the problem into pieces and solve each piece until we arrive at the answer.
the formula for the surface area of the cube is:
SA = 6s^2; s is the length of one side of the cube
for the 3-inch cube
SA = 6(3^2)
SA = 6(9)
SA = 54 in^2
note however, that the actual surface area is less the area occupied by the 2-inch cube place on the 3-inch cube, which is
A = s^2; since this is a square
A = 2^2
A = 4 in^2
the actual SA (aSA) therefore of the 3-inch cube is
aSA = 54 - 4 = 50 in^2
for the 2-inch cube
SA = 6s^2
SA = 6(2^2)
SA = 6(4)
SA = 24 in^2
to solve for the actual SA of the 2-inch cube, we subtract the area which is in contact with the 3-inch cube and the 1-inch cube
aSA = 24 - 2^2 - 1^2
aSA = 24 - 4 - 1
aSA = 19 in^2
for the 1-inch cube
SA = 6s^2
SA = 6(1^2)
SA = 6 in^2
the actual surface area is less the area in contact with the 2-inch cube
aSA = 6 - 1^2
aSA = 5 in^2
the surface area of the three cube tower will just be the sum of the aSA of the three cubes
SA = 50 + 19 + 5
SA = 74 in^2 ans
Step-by-step explanation:
