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State true or false.

The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the given figure is $π r 2 3 [3 h − 2 r]$ .

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True

False

answer is A.

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Detailed Solution

Given figure is,
Question Image

We know, the volume of the cylinder =

π r 2 h

.
And the volume of the hemisphere is,

V = 23 π r 3

In the given figure capacity of the cylindrical vessel with a hemispherical portion raised upward at the bottom is equal to the volume of the hemisphere subtracted from the volume of the cylinder. So,

V = π r 2 h − 23 π r 3 V = π r 2 3 3 h − 2 r

Therefore, 1 is the correct option and the statement is true.

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