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Asked by Dev | 06 Mar, 2019, 09:06: PM
If the cone radius is 9cm, its height is 12 cm, then slant height AC as shown in figure can be calculated as 15 cm.

When the sphere just touches the cone at D, then OD is normal at D. ΔODC and ΔOEC are congruent.  DC = EC = 9 cm

in ΔOAD,  OA = (12-r) cm, OD = r cm.   Hence (12-r)2 = r2 + 62  or  144 +r2 -24r = r2 + 36    or  108 - 24r = 0   or  r = 4.5 cm

volume of water that overflows = volume of sphere = (4/3)π(9/2)3  ≈ 382 cm3

volume of water in the cone (before immersing sphere) = (1/3)π×9×9×12 = 1018 cm3

Fraction of water that overflows = 382/1018 = 0.375
Answered by Thiyagarajan K | 06 Mar, 2019, 11:43: PM

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