Question
A solid cylinder of radius 7 cm and height 10 cm is
melted and recast into small solid cones each of radius 3.5 cm and height 8 cm. Find how many such cones are formed.Solution
ATQ,
Volume of cylinder = πr²h = π × 7² × 10 = π × 49 × 10 = 490π cm³ Volume of one cone = (1/3)πr²h = (1/3)π × 3.5² × 8 = (1/3)π × 12.25 × 8 = (1/3)π × 98 = (98/3)π cm³ Number of cones = (Volume of cylinder) / (Volume of one cone) = 490π / ((98/3)π) = 490 × (3/98) = 5 × 3 = 15
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