This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — 1. Step 1: Analyze the structure of the model and the painting rules. The model consists of 6 cubes. The top and bottom surfaces of the entire model are white. All other exterior vertical surfaces are painted grey. Any internal faces (touching another cube) are unpainted. Let's identify each cube and count its grey faces: Cube 1 (bottom left, under a top cube): Has 3 exposed vertical faces (Front, Back, Left). Its top is covered, its bottom is white, and its right face touches another cube. So, 3 grey faces. Cube 2 (bottom middle, under a top cube): Has 2 exposed vertical faces (Front, Back). Its top is covered, its bottom is white, and its left and right faces touch other cubes. So, 2 grey faces. Cube 3 (bottom middle, next to Cube 2): Has 3 exposed vertical faces (Front, Back, Right). Its top is exposed (white), its bottom is white, and its left face touches another cube. So, 3 grey faces. Cube 4 (bottom right): Has 3 exposed vertical faces (Front, Back, Right). Its top is exposed (white), its bottom is white, and its left face touches another cube. So, 3 grey faces. Cube 5 (top left): Has 3 exposed vertical faces (Front, Back, Left). Its top is exposed (white), its bottom touches another cube, and its right face touches another cube. So, 3 grey faces. Cube 6 (top right): Has 3 exposed vertical faces (Front, Back, Right). Its top is exposed (white), its bottom touches another cube, and its left face touches another cube. So, 3 grey faces. Step 2: Count how many cubes have exactly two faces painted grey. From the analysis above, only Cube 2 has exactly two faces painted grey. The number of cubes with exactly two faces painted grey is 1. 2. Step 1: Understand the definition of "one pair of parallel sides". A shape with exactly one pair of parallel sides is a trapezium (also known as a trapezoid). Step 2: Examine each shape on the grid. Shape A: The top and bottom sides are horizontal, making them parallel. The other two sides are not parallel. Thus, Shape A has one pair of parallel sides. Shape B: This is a hexagon. None of its sides appear to be parallel to each other. *