A solid metallic sphere of radius 12cm is melted and recast into a number of small cones ,each of radius 4cm and height 3cm. find the number of cones so formed.
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6
volume of sphere=4/3πr ³⇒4/3.22/7.12.12.12 = 7233.6 cm cube
volume of cone = 1/3πr²h⇒50.2
let'x' be the no. of cones
volume of X no.of cones = volume of sphere
50.2 × X = 7233.6
X = 7233.6/50.2
=144.0
so we can make 144 cones with given sphere
volume of cone = 1/3πr²h⇒50.2
let'x' be the no. of cones
volume of X no.of cones = volume of sphere
50.2 × X = 7233.6
X = 7233.6/50.2
=144.0
so we can make 144 cones with given sphere
Answered by
7
volume of sphere = total volume of cones
volume of sphere = (4/3)πR³ = (4/3)π×(12)³ = 2304π cm³
volume of one cone = (1/3)πr²h = (1/3)π×(4)²×3 = 16π cm³
∵volume of sphere = n× volume of one cone
⇒n = 2304π/16π = 144 cones
volume of sphere = (4/3)πR³ = (4/3)π×(12)³ = 2304π cm³
volume of one cone = (1/3)πr²h = (1/3)π×(4)²×3 = 16π cm³
∵volume of sphere = n× volume of one cone
⇒n = 2304π/16π = 144 cones
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