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Question
Find the number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metallic cylinder of height 45 cm and diameter 4 cm.
Solution
We have,
Radius of the sphere, R `= 6/2 = 3 "cm" `
Radius of the cylinder, `"r" = 4/2 = 2 "cm"` and
Height of the cylinder, h = 45 cm
Now,
The number of solid spheres`= "Volume of the cylinder"/"Volume of the sphere"`
`=(pi"r"^2"h")/((4/3pi"R"^3))`
`=(3"r"^2"h")/(4"R"^3)`
`=(3xx2xx2xx45)/(4xx3xx3xx3)`
= 5
So, the number of solid spheres so moulded is 5.
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