Question

正四面体的棱长为a，它的体积为______．

Answer 1

正四面体的底面积为s= 1 2 a 2 × 3 2 = 3 4 a 2
正四面体的底面半径为r= 3 2 a × 2 3 = 3 3 a
∴正四面体的高H= a 2 - r 2 = a 2 - 1 3 a 2 = 6 3 a
∴正四面体的体积为V= 1 3 sH= 1 3 × 3 4 a 2 × 6 3 a = 2 12 a 3
故答案为 2 12 a 3