<p>A large solid cube is assembled by gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small blocks that make up the large cube have no red paint on them, how many small cubic blocks make up the large cube?</p>
<p>is the answer 125?</p>
<p>That’s what I think it is…</p>
<p>Shouldn’t you have the answer key to the test?</p>
<p>125 is correct. A 3x3x3 inner core of unpainted cubes must be covered on all sides by more cubes that are painted. Each dimension of the larger cube must be increased by 2 in order to cover the inner core, 5x5x5 = 125.</p>
<p>The correct answer is 125. The core of the large cube is a 27 cube of unpainted blocks, or a cube with length, width, and height 3. Around this core is a shell of blocks, one block thick, all of which are painted. This shell adds 1 block to each side of the core cube, or 2 blocks total to each dimension of the core cube, making the length, width, and height of the large cube each equal to 5. A cube of this size is made up of 5^3 = 125blocks.</p>