问题 解答题

已知圆锥的侧面积为12π,

(1)求圆锥的母线l关于底面半径r的函数关系式,并求出r的取值范围;

(2)当圆锥的全面积为16π时,求圆锥的侧面展开图的圆心角度数.

答案

(1)由题意得:12π=π×r×l,

∴l=

12
r
(0<l<2
3
);

(2)∵圆锥的侧面积为12π,圆锥的全面积为16π,

∴圆锥的底面积为4π,

∴圆锥的底面半径为4π÷2π=2,

∴圆锥的母线长为:侧面积÷π÷底面半径=6,

设圆锥的圆心角为n,则:

62
360
=12π,

解得n=120.

完形填空

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判断题