Question
A cylinder is inscribed in a sphere. The radius of the
sphere is 5/6 times the height of the cylinder. What is the ratio of the volume of the cylinder to the volume of the sphere?Solution
The radius of the sphere is 5/6 times the height of the cylinder. The radius of the sphere = 5 The height of the cylinder = 6 Now, According to the figure (Radius of cylinder) ² = (5) ² - (3)2 (Radius of cylinder) ² = (25-9) (Radius of cylinder) ² = 16 Radius of cylinder = 4 Now, Volume of cylinder/Volume of sphere = πr²h/4/3 πι³ 3 = [π × (4)2 × 6]/ [4/3 × π × (5)3] = (16 x 6)/ (4/3 x 125) = 96/500/3 =96×3:500 =72:125
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