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प्रश्न
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
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उत्तर
For sphere, radius = R = 15 cm
For cone, radius = r = 2.5 cm, height, h = 8 cm
Let the number of cones recast be n.
∴ n x Volume of one cone = Volume of solid sphere
`=> n xx 1/3 pir^2h`
= `4/3pir^3`
`n × 1/3 π(2.5)^2(8) = 4/3π(15)^3`
Now multiply both sides by 3 (this is the “missing” step you’re thinking of):
`=> nπ xx (2.5)^2 xx (8) = 4π xx (15)^3` ...[Cancel π from both sides]
`=> n = (4 xx 15 xx 15 xx 15)/(2.5 xx 2.5 xx 8)`
`=> n = 270`
Thus, 270 cones were recast.
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