Small big cuboid. The surface area of this cuboid is (2) 1cm, which is combined into a cuboid. The surface area of this cuboid is (2) square cm.
(3) In the figure below, 1 cube represents 1 cubic centimeter, and then () such cubes can be added to form a cube with a side length of 3 cm.
[Solution] (1)42 square centimeters.
(2)? 10。 (3) 13。
[Common Errors]
(1)66 or 58 or 54 square centimeters.
(2) 12。 (3) 18。
[analysis]
These questions mainly examine students' spatial imagination ability, which is difficult to answer. (1) The surface area of a cuboid (as shown on the left below) is (6+3+2)×2=22 (square centimeter). What is the total surface area of three cuboids? 22×3=66 (square centimeter); If the surface area of three cuboids is (6+3)×2×3+2×2=58 (square centimeter); If the surface area of three cuboids is (6+2)×2×3+3×2=54 (square centimeter); If the surface area of a cuboid formed by splicing the faces of three cuboids is (3+2)×2×3+6×2=42 (square centimeter), the surface area of the last spelling is the smallest, and other spellings are not the smallest.
(2) I forgot to remove two 1 cm2 in the middle (as shown on the right above), so I mistakenly thought it was 12 cm2.
(3) The correct answer to the question should be the number of small cubes contained in a large cube with a length of 3 cm.
(27) Subtract the original number of small cubes, the original number of small cubes is 14, but only nine are drawn in the figure, and the remaining five are covered. If you don't consider these five, there will be an error of 27-9= 18 (pieces).
The formation of spatial imagination needs to be gradually cultivated, generally through intuitive training first, and then transition to abstract imagination.