There are cubes of ① and ② as shown in a figure below.
Cube ① is assembled with 8 pieces of small size cubes and cube ② is assembled with 27 pieces of small size cubes with the same small size.
Answer to the following questions.
(1) When you cut cube ① by the plane which passes along the three points A, B, and C, answer the name of the figure of a cut surface as correctly as possible.
(2) When you cut cube ① by the plane which passes along the three points A, B, and C, answer the number of the small cubes cut.
(3) When you cut cube ② by the plane which passes along the three points A, B, and C, answer the number of the small cubes cut.
Answer
(1) Rhombus
(2) 6
(3) 15
Solution
(1) The cut surface is as shown in the figure below, this figure is a rhombus.
(2) The number of cubes being cut can be expressed as shown below figure.
There are three pieces both in an upper and a lower step, so there are six pieces altogether.
(3) The number of cubes being cut can be expressed as shown below figure.
There are four pieces in an upper step, seven in a middle step and four in a lower step, so there are 15 pieces altogether.
