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Question
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
Options
True
False
Solution
This statement is True.
Explanation:
Let r be the radius of the sphere and cylinder.
Given that height of the cylinder = diameter of the sphere.
`\implies` h = 2r
According to the question,
Volume of a sphere = `2/3` × volume of cylinder
`\implies 4/3 pir^3 = 2/3 xx pir^2 xx 2r` ...[∵ h = 2r]
`\implies 4/3 pir^3 = 4/3 pir^3`
Hence, the volume of a sphere is equal to two-third of the volume of a cylinder.
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