Ziwei Huapa

Because PA, PB and PC are perpendicular to each other and PA=PB=PC=a, AB=BC=AC=√2a can be calculated.

The vertical line of the plane ABC passing through point P must pass through the center D and the center O of the triangle ABC, and calculate AD=√6/3 a,

Let the radius of the ball be R, then PD+DO = R, PD 2+AD 2 = A 2, AD 2+DO 2 = R 2, and calculate the radius R = √ 3/2 a..

Sphere = 4 π r 2 = 3 π a?

It is best to refer to Lagerstroemia speciosa.