📝 题目
6. 4.1 求环面 $x = \left( {b + a\cos \varphi }\right) \cos \theta ,y = \left( {b + a\cos \varphi }\right) \sin \theta ,z = a\sin \varphi (0 < a <$ $b)$ 被两条经线 $\theta = {\theta }_{1},\theta = {\theta }_{2}$ 和两条纬线 $\varphi = {\varphi }_{1},\varphi = {\varphi }_{2}$ 所围成的那部分面积,并求出整个环面面积.
💡 答案与解析
6. 4.1 ${a}\left( {{\theta }_{2} - {\theta }_{1}}\right) \left\lbrack {b\left( {{\varphi }_{2} - {\varphi }_{1}}\right) + a\left( {\sin {\varphi }_{2} - \sin {\varphi }_{1}}\right) }\right\rbrack$ .