Nadia builds a solid using unit cubes. Looking from the front, the left column is 3 unit cubes tall and the right column is 2 unit cubes tall. Looking from the right side, the front row is 3 unit cubes tall and the back row is 2 unit cubes tall. What is the MINIMUM number of unit cubes needed to build a solid that matches BOTH views?
Show Worked Solution
Worked Solution
Step 1: Set up a 2 × 2 grid (2 columns wide, 2 rows deep).
Step 2: For each cell, the height must be at least as tall as shown in BOTH the front view AND the side view. Take the MAXIMUM of the two view heights for each cell.
Front view: Left column = 3, Right column = 2
Side view: Front row = 3, Back row = 2
Cell (front-left): max(3, 3) = 3 cubes
Cell (front-right): max(2, 3) = 3 cubes
Cell (back-left): max(3, 2) = 3 cubes
Cell (back-right): max(2, 2) = 2 cubes
Step 3: Add all cells.
3 + 3 + 3 + 2 = 11
Minimum number of unit cubes = 11
Correct answer: 11
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