Two cubes of volumes 8cm3 and 27cm3 are glued together at their faces to form a solid with the smallest possible surface area. What is the number of square centimeters in the surface area of the resulting solid

70

Step-by-step explanation:

First, we note that the cubes of volume 8 and 27 must have edges of length 2 and 3, respectively.

If not joined, total area is 78

The maximum concealed surface area is an entire face of the 2-cube, on both solids: 2*4 = 8

So, the minimum exposed area would be 78-8 = 70

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).