A medium question on solids for P5–P6, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P5 and P6 first rounds and finals: painted small cubes, water levels and the surface area of stacks.
The question
9 small cubes with edges of 1 cm are stacked as shown.
It stands on the floor, and every face that shows is painted (not the bottom, which is on the floor).
What area is painted, in cm²?
Show the hints (2)
💡Hint 1: Don't go cube by cube. How many squares do you see from the top, the front and the right?
💡Hint 2: Which way do the faces that can't be painted face?
Worked solution
Have a go first, then read the solution step by step.
1.From the top you see 6 squares (the bottom isn't painted).
2.From the front you see 5 (and as many from the back).
3.From the right you see 6 (and as many from the left).
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