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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. State true or false.

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False

True

answer is A.

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Detailed Solution

Given, the height of the cylinder = diameter of the sphere.
We know that diameter is double of radius.
So, the height of the cylinder is,

h = 2 r

Now let’s find the volume of the cylinder.
The formula of the volume of the cylinder

= π r 2 h

⇒

π r 2 (2 r)

⇒ 2 π r 3

The formula of the volume of the sphere,

V = 43 π r 3

.
It can be written as,

23 (2 π r 3)

.
Hence, the volume of a sphere is equal to two-third of the volume of a cylinder.
Therefore, the given statement is true.

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