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Question
A metallic solid sphere of radius 10.5 cm is melted and recasted into smaller solid cones, each of radius 3.5 cm and height 3 cm. How many cones will be made?
Solution
Let the number of cones formed be n.
Radius of sphere, r = 10.5 cm
Volume of sphere, `V_1 = 4/3pir^3`
`=>V_1 = 4/3pi(10.5)^3 "cm"^3`
Height of cone, h = 3 cm and radius of cone, R = 3.5 cm
∴ Volume of each smaller cone, `V2 = 1/3pir^2h`
`=> V_2 = 1/3 pi (3.5)^2 xx 3 "cm"^3`
It is given that the solid sphere is melted and recast into smaller cones.
So, n × Volume of each smaller cone = Volume of the sphere
`:. n xx 1/3 pi (3.5)^2 xx 3 = 4/3 pi(10.5)^3`
`=> n = (4 xx (10.5)^3)/((3.5)^2 xx 3)`
`=> n = 126`
Thus, the number of smaller cones formed is 126
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