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Question
A solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm.Find the number of cones so formed.
Solution
Let the number of cones formed be n.
Given: Radius of sphere, r = 10.5 cm
Volume of sphere`V_1=pi_3^4-r^3`
`rArrV rpi_3^4-(10.5)cm^3`
Given: Height of cone, h = 3 cm and radius of cone, R = 3.5 cm
`therefore` Volume of each smaller come `v_2=1/3piR^2h`
`rArr V_2=1/3pi(3.5)^2xx3cm^3`
Since the solid sphere is melted and recast into smaller cones,
n × Volume of each smaller cone = Volume of the sphere
`thereforenxx1/3 pi (3.5)^2xx3=4/3pi(10.5)^3`
`rArrn=(4xx(10.5)^3)/((3.5)^2xx3)`
`rArrn=126`
Thus, the number of smaller cones formed is 126.
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