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Question
A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.
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Solution
Diameter of sphere = 21 cm
Radius of sphere =`21/2` cm
Volume of sphere `= 4/3 pir^3 = (4xx21xx21xx21xx21pi)/(3xx2xx2xx2)= (21xx21xx21pi)/(3xx2) "cm"^3`
Diameter of the cone = 3.5 cm
Radius of the cone `= 3.5/2 = 7/4 "cm"`
Height = 3 cm
Volume of each cone` = 1/3pir^2h xx 1/3pixx3xx(7/4)^2 = (7/4)^2 pi "cm"^3 `
`"Total number of cones"= "Volume of sphere"/"Volume of a cone" = ((21xx21xx21pi)/(3xx2))/((7/4)^2pi) = (21xx21xx21xxpixx4xx4)/3xx2xxpixx)`
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