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Volume of cone = (1/3)Pi x r^2h = (1/3)Pi x 5^2 x 12 = 100 Pi Volume of sphere = (4/3)Pi x 6^3=128 Pi You can find the ratio of volumes = 128/100=32/25
Let the radius of the sphere = r cm.OD = OE = rHeight of the cone EA = 12 cmSlant height AC = √{ 52 + 122 } = √169 = 13 cm.In ΔAEC and ODA we have∠AEC = ∠ODA = 90°⇒ ΔAEC ≃ ODA [ AA similarity ] ⇒ OD / OA = EC / AC⇒ r / ( 12 - r) = 5 / 13⇒ r = 10 / 3 cm∴ Volume of the sphere / Volume of the cone = ( 4/3)πr3 / (1/3)πr2h= (4 x 10/3 x 10/3 x 10/3) / (5x5x12)= 40 / 81Volume of the sphere : Volume of the cone= 40 : 81
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