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ICSE Class 10 Answered

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Asked by Dev | 06 Mar, 2019, 09:06: PM
answered-by-expert Expert Answer
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
 
Hence AD = 6 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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