Question

142 Chapter 8. Algebraic Thinking EXTENSION 1. Unit cubes are used to build a larger cube that has edges 3 units long. Then the six faces of the larger cube are painted. When this cube is taken apart, how many of the unit cubes will have exactly 3 painted faces? 2 painted faces? I painted face? no painted faces? This unit cube has exactly 3 painted faces 2. Repeat Exercise 1 for cubes with edges 4 units and 5 units long. Record your results in the table. 3 units 4 units 5 units n units Length of edge 3 painted faces 2 painted faces 1 painted face O painted faces Number of unit cubes with 3. Look for patterns that lead to expressions that represent the number of unit cubes with 3 painted faces, 2 painted faces, 1 painted face, and no painted faces in a cube with an edge n units long. Write the expressions in the table. 4. a. What is the length of an edge of a large cube made up of 729 unit cubes? b. How many of the unit cubes will have 3 painted faces? 2 painted faces? 1 painted face? no painted faces? 5. Explain what each of your expressions in Exercise 3 represents physically with the cubes.

I don't really undertand what the problems are asking me can someone help?

Answer 1

Mit cubes & Lx 1 x 1 units. They build a larger cube 3x3x3 units = 27 units Total cubes required. 27. 27 sq cubes 6 faces painted Whit cuber with faces painted cube at edges Mnit cubes arth Corner 2 & cubes . 2 faces painted There are a total of 3 cubes on rech edge There are 12 edges 12 (3-2) 2 12 cubes. Muit cubes with I fece paunted & Cube as each face 23x 329 But edges have 2 or more painted faces. Wence red (3-2) ² 1 cube There are 6 faces , 6x1 a 6 cubes. No pain tad faces : 827 - (6+ 12 + 8) 1 cube

3 units 4 unita 5 ta 3 painted 12(2-2) 2 pansted 36 12 4 54 I paunted (h-2) 6 24 painted 1 a 27 n-fblas / n²-{(6x-2)) + 12 (n-2) +87 729 unit cubes cube e of large 67 length of an 729 unit 2 qunit 3 kces. 8 (painted) 2 faces. 12 x (9-2) 284 (partea) I face . 294 (pausted) face ? 24 g (non paunted). 343