There are white and black cubes whose one side is 1 cm.
63 white cubes and 62 black cubes are arranged in by turns as shown in lower Fig. 1 and a large cube is made.
Furthermore, this large cube is cut so that it may pass along three point A, B, and C.
Answer the following questions.
Noted that the volume of a triangular pyramid is calculated by the formula of (the area of the bottom) × (height) / 3.
(1) Draw the situation of the cut face in the lower Fig. 2.
(2) Find the ratio of the volume of a solid including the point D to the volume of the original large cube.
(3) Find the number of white cube in a solid including the point D which is not cut.
Answer
(1)
(2) 1 : 6
(3) 7 pieces
Solution
(1)
According to the figures below, cut face is to be the picture of answer.
(2)
The volume of a solid including the point D = 5 × 5 / 2 × 5 /3 = 125/6 cm3.
The volume of the original large cube = 5 × 5 × 5 = 125 cm3.
125/6 : 125 = 1 : 6
(3)
Solid line shows the cut line of upper face and dotted line shows the cut line of lower face.
Square with circle mark shows the cube not cut.
