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Question
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.
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Solution
Let the number of cones be n.
Let the radius of the sphere be rs = 6 cm
Radius of a cone is rc = 2 cm
And the height of the cone is h = 3 cm
Since the cones are melted and recast into a sphere, the total volume remains the same.
Therefore, the volume of the sphere = n × the volume of one cone.
`=> 4/3 pir_s^3 = n(1/3 pir_c^2h)`
`=> (4r_s^3)/(r_c^2h) = n`
`=> n = (4(6)^3)/((2)^2(3))`
`=> n = (4 xx 216)/(4 xx 3)`
n = 72
Hence, the number of cones is 72.
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