已知球O的面上四点A,B,C,D,DA⊥平面ABC.AB⊥BC,DA=AB=BC=,则球O的体积等于?
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![已知球O的面上四点A,B,C,D,DA⊥平面ABC.AB⊥BC,DA=AB=BC=,则球O的体积等于?](/uploads/image/z/8578938-66-8.jpg?t=%E5%B7%B2%E7%9F%A5%E7%90%83O%E7%9A%84%E9%9D%A2%E4%B8%8A%E5%9B%9B%E7%82%B9A%2CB%2CC%2CD%2CDA%E2%8A%A5%E5%B9%B3%E9%9D%A2ABC.AB%E2%8A%A5BC%2CDA%3DAB%3DBC%3D%2C%E5%88%99%E7%90%83O%E7%9A%84%E4%BD%93%E7%A7%AF%E7%AD%89%E4%BA%8E%3F)
已知球O的面上四点A,B,C,D,DA⊥平面ABC.AB⊥BC,DA=AB=BC=,则球O的体积等于?
已知球O的面上四点A,B,C,D,DA⊥平面ABC.AB⊥BC,DA=AB=BC=,则球O的体积等于?
已知球O的面上四点A,B,C,D,DA⊥平面ABC.AB⊥BC,DA=AB=BC=,则球O的体积等于?
设 DA=AB=BC=a
ABC外接圆的半径:r=a/√2
球的半径:R^2=1/2 *a^2 + 1/4 * a^2 = 3/4 * a^2 即 :R = √3/2 * a
球的体积:V = 4/3 * π * R^3 = √3/2 * π * a^3
∵DA=AB=BC=√2,且AB⊥BC∴AC=2,DA=√2又∵DA⊥平面ABC∴DC=√6根据球的体积V=4/3兀的立方得出球的体积为√6兀
,DA=AB=BC=a, r=a√3/2, V=4π*R^3/3=V=√3π*a^3/2
,DA=AB=BC=a, r=a√3/2, V=4π*R^3/3=V=√3π*a^3/2
设 DA=AB=BC=a
ABC外接圆的半径:r=a/√2
球的半径:R^2=1/2 *a^2 + 1/4 * a^2 = 3/4 * a^2 即 : R = √3/2 * a
球的体积:V = 4/3 * π * R^3 = √3/2 * π * a^3
设 DA=AB=BC=a
r=a/√2(ABC外接圆的半径)
球的半径:R^2=1/2 *a^2 + 1/4 * a^2 = 3/4 * a^2 即 : R = √3/2 * a
球的体积:V = 4/3 * π * R^3 = √3/2 * π * a^3