https://spherical-harmonics.hateblo.jp/entry/2025/01/21/164123

2025.01.21記

[1] From an elliptical plate with the major axis $2a=20$ c.m. and the minor axis $2b=10$ c.m. is required to get two discs of equal diameters. Calculate the gratest possible diameter $2t$ of the discs.

[2] A plane cuts a sphere of the radius $r=8$ c.m. into two partes. What is the distance of the plane from the centre of the sphere, if the ratio of the surface area should be $1:4$ .

[3] A cylindrical hole of the diameter a is bored through the center of a ball of radius $b$ ; find the volume of the hole.

[4] Any straight line $\rm AB$ drawn through a fixed point $\mbox{A}(p，0)$ cuts the $y$ -axis at a point $\rm B$ . Find the envelope of $\rm BC$ perpendicular to $\rm AB$ .