Thread: More Word Problems! Help!!

6. A 2-by-4-by-8 rectangular solid is painted red. It is cut into unit cubes and reassembled into a 4-by-4-by-4 cube. If the entire surface of this cube is red, how many painted unit-cube faces are hidden in the interior cube?


7. If a year has 364 days, then the same calendar could be used every year by only changing the year. A "regular" year has 365 days and a leap year has 366 days. The year 2000 has a leap year and leap years occur every 4 years between the years 2000 and 2100. Claudia has calendar for 2009. What will be the next year that she can use this calendar by merely changing the year?






8. A 6-question True-False test has True as the correct answer for at least 2/3 of the questions. How many different true/False answer patterns are possible on an answer key for this test?

Hello, Brent!

It's simple arithmetic . . .

6. A 2-by-4-by-8 rectangular solid is painted red.
It is cut into unit cubes and reassembled into a 4-by-4-by-4 cube.
If the entire surface of this cube is red,
how many painted unit-cube faces are hidden in the interior cube?

Code:

                 8
          * - - - - - - *
         /             /|
      4 /             / | 2
       /             /  |
      * - - - - - - *   *
      |             |  /
    2 |             | / 4
      |             |/
      * - - - - - - *
             8

The total surface area is:

. .

There are 112 red faces on the sixty-four unit cubes.

Code:

          * - - - - *
         /         /|
       4/         / |
       /         /  | 4
      * - - - - *   |
      |         |   *
    4 |         |  /
      |         | /4
      |         |/
      * - - - - *
           4

The total surface area of the cube is: .

There are 96 red faces on the outside of the cube.


Therefore, there are: . red faces hidden inside.