Page 64 - NUMINO Challenge_D2
P. 64
Basic Concepts The Maximum and Minimum Number of Stacked Cubes
It is possible to guess the shape of the stacked cubes by studying the top,
front, and side views of a solid figure. Several possible shapes can be made as
shown below.
Top Front Side
9 cubes 10 cubes 11 cubes
Example The following shows the top, front, and side views of the stacked
cubes. Find the maximum and minimum numbers of cubes used to
make the solid figure.
Class Notes Top Front Side
Write the number of cubes in each column from the front view at the 11
bottom of the top view. Write the number of cubes in each column from 1 2
the side view on the side of the top view. Then, first write the number 33
of cubes inside the squares that are certain. 13 2
In the case where the maximum number of cubes is used, two cubes are
stacked for each colored space. Write the number of cubes in the colored spaces in the
case where the minimum number of cubes is used.
Maximum Minimum Number of
Number of Cubes Used Cubes Used
11 11
122 2 12
32 3 33
13 2 13 2
Therefore, the maximum number of cubes used is , and the minimum number of
cubes used is .
61Geometry
It is possible to guess the shape of the stacked cubes by studying the top,
front, and side views of a solid figure. Several possible shapes can be made as
shown below.
Top Front Side
9 cubes 10 cubes 11 cubes
Example The following shows the top, front, and side views of the stacked
cubes. Find the maximum and minimum numbers of cubes used to
make the solid figure.
Class Notes Top Front Side
Write the number of cubes in each column from the front view at the 11
bottom of the top view. Write the number of cubes in each column from 1 2
the side view on the side of the top view. Then, first write the number 33
of cubes inside the squares that are certain. 13 2
In the case where the maximum number of cubes is used, two cubes are
stacked for each colored space. Write the number of cubes in the colored spaces in the
case where the minimum number of cubes is used.
Maximum Minimum Number of
Number of Cubes Used Cubes Used
11 11
122 2 12
32 3 33
13 2 13 2
Therefore, the maximum number of cubes used is , and the minimum number of
cubes used is .
61Geometry
