504 cones, each of diameter 3.5 cm height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.

Explanation

`"Radius of each cone, "r=(3.5/2)cm=(35/20)cm=7/4cm`.
`"Height of each cone, h = 3 cm".`
`"Volume of the each cone"=1/3pir^(2)h`
`=(1/3xxpixx7/4xx7/4xx3)cm^(3)=((94pi)/16)cm^(3)`
Total voluem of 504 cones
`=((49pi)/16xx504)cm^(3)=((49pixx63)/2)cm^(3).`
Let the radius of the sphere be R.
Then, volume of the sphere `=4/3 piR^(3)`.
Volume of the sphere = total volume of 504 cones
`rArr4/3piR^(3)=(49pixx63)/2rArrR^(3)=(49xx63)/2xx3/4)`
`rArrR^(3)=((7xx7xx7xx9xx3)/(2xx4))rArrR=((7xx3)/2)cm=21/2cm.`
`"Diameter of the sphere "=(21/2xx2)cm=21cm.`
`"Surface area of the sphere "=4piR^(2)=(4xx22/7xx21/2xx21/2) cm^(2)`
`=1386 cm^(2)`