If a sphere is placed in a cone of height 9 cms as shown in figure, then the volume of sphere if it touches lateral surface and base of cone is
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Volume of sphere is 36πcm²
Height of sphere = 9cm (Given)
In ΔOCD
∠COD=30°
Therefore, sin 30° = CD/DO = 1/2 = CD/9
CD = 4.5cm
Since, ΔOAB∼ΔOCD
OA/OC = AB/CD
= 9 - AB/9 = AB/4.5
= 40.5 - 4.5AD = 9AB = 13.5AB = 40.5
= AB = 40.5/13.5 = 3cm
Volume of sphere
4/3πr² = 4/3 × π × 3 × 3 × 3
= 36πcm²
Therefore, the volume of sphere is 36πcm².
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