This GMAT quant practice question is from the topic Mensuration (Solid Geometry): Concept covered is properties of cubes.
Question 10: A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
When a 5 cubic centimeter cube is sliced into 1 cubic centimeter cubes, we will get 5 × 5 × 5 = 125 cubes of 1 cubic centimeter.
In each side of the larger cube, the smaller cubes on the edges will have more than one of their sides painted.
Therefore, the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted.
In each face of the larger cube, there will be 5 × 5 = 25 cubes.
Of these, the cubes on the outer rows will be on the edge. 16 such cubes exist on each face.
If we count out the two outer rows on either side of a face of the cube, we will be left with 3 × 3 = 9 cubes which are not on the edge in each face of the cube.
Therefore, there will be 9 cubes of 1-cc volume per face that will have exactly one of their sides painted.
In total, there will be 9 × 6 = 54 such cubes.
GMAT® is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.
GRE® is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.
SAT® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.
Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
14B/1 Dr Thirumurthy Nagar 1st Street
Chennai 600 034. India