504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.
No. of cones = 504
Diameter of a cone = 3.5 cm
Radius of the cone, r = 1.75 cm
Height of the cone, h = 3 cm
Volume of a cone
`=1/3xxpixx3.5/2xx3.5/2xx3 " cm"^2`
Volume of 504 cones
`=504xx1/3xxpixx3.5/2xx3.5/2xx3 " cm"^2`
Let the radius of the new sphere be ‘R’.
Volume of the sphere `=4/3 pir^3 `
Volume of 504 cones = Volume of the sphere
Radius of the new sphere = 10.5 cm