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我们知道,球内接圆柱、圆锥的侧面积与体积存在最大值,而球外切圆柱、圆锥的侧面积与体积存在最小值,那么,球内接、外切圆台的侧面积与体积是否存在最大或最小值呢?本文拟通过对角参数的适当选取,解决这一问题。问题1 设球的半径为R,求球内接圆台的侧面积与体积的最大值。解如图1,等腰梯形ABCD为球内接圆台的轴截面,EF过球心O且与BC垂直,设∠EOD=α,∠FOC=β,圆台的上、下底半径、高及母线长则分别为
We know that there are maximum values in the area and volume of the cylinder and cone connected to the ball, and there is a minimum value for the area and volume of the cylinder and cone outside the sphere. Then, does the lateral area and volume of the ball inscribed and circumscribed circular table exist? What is the maximum or minimum value? This paper intends to solve this problem by proper selection of diagonal parameters. Question 1 Let R be the radius of the ball. Find the side area and volume of the ball inscribed in the circular table. The solution is shown in Fig.1. The isosceles trapezoid ABCD is the axial section of the ball inscribed circle table. EF crosses the center of the sphere O and is perpendicular to BC. Let ∠EOD=α, ∠FOC=β, the radius of the upper and lower bases of the circular table, height and busbars. The lengths are