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Question
The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:
Options
3
5
4
6
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Solution
Let r and h be the radius and the height of the cylinder, respectively.
Given:
Diameter of the cylinder = 4 cm
∴ Radius of the cylinder, r = 2 cm
Height of the cylinder, h = 45 cm
Volume of the solid cylinder = `pir^2h=pixx(2)^2xx45 cm^2=180pi cm^3`
Suppose the radius of each sphere be R cm.
Diameter of the sphere = 6 cm
∴ Radius of the sphere, R = 3 cm
Let n be the number of solids formed by melting the solid metallic cylinder.
∴ n × Volume of the solid spheres = Volume of the solid cylinder
`=>nxx4/3 pi R^3=180pi`
`=>nxx4/3 pi(3)^3=180pi`
`=>n=(180xx3)/(4xx27)=5`
Thus, the number of solid spheres that can be formed is 5.
Hence, the correct option is B.
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