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Question
A solid piece of iron in the form a cuboid of dimensions (49 cm × 33 cm × 24 cm) is moulded into a solid sphere. The radius of the sphere is ______.
Options
19 cm
21 cm
23 cm
25 cm
Solution
A solid piece of iron in the form a cuboid of dimensions (49 cm × 33 cm × 24 cm) is moulded into a solid sphere. The radius of the sphere is 21 cm.
Explanation:
Volume of the cuboid = (l × b × h) = 49 × 33 × 24 cm3
Let the radius of the sphere`=4/3`
The volume of the sphere and the cuboid are the same.
Therefore,
`4/3 pi"r"^3 = l × b × h`
`=> 4/3xx22/7xx"r"^3=49xx33xx24`
`=> "r"^3 = 49xx33xx24xx21/88`
`=> "r"^3 = 21xx21xx21`
`=> "r"^3 = (21)^3`
⇒ r = 21 cm
Hence, the radius of the sphere is 21 cm.
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