The following log is processed into the largest square log. The length of the log is 1.5m and the diameter of its bottom surface is 10cm. What is the volume of the square log? (2) How many cubic decimeters of wood become waste in the processing?

The following log is processed into the largest square log. The length of the log is 1.5m and the diameter of its bottom surface is 10cm. What is the volume of the square log? (2) How many cubic decimeters of wood become waste in the processing?

1.5m = 15m
10 cm = 1 decimeter
Bottom radius of log = 1 △ 2 = 0.5 (decimeter)
The two diagonals of the largest square wood divide it into four isosceles right triangles of equal area,
Bottom area of square timber
=The sum of the areas of four isosceles right triangles
=(0.5×0.5÷2)×4
=0.125×4
=0.5 (square decimeter)
Volume of square wood
=0.5×15
=7.5 (cubic decimeter)
The volume of wood that becomes waste during processing
=Log volume - the volume of the largest square log
=3.14×0.5×0.5×15-7.5
=11.775-7.5
=4.275 (M3)