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प्रश्न
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom, as shown in figure, is ______.
रिकाम्या जागा भरा
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उत्तर
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom, as shown in figure, is `underlinebb(1/3 πr^2 (3h - 2r))` .
Explanation:
Volume of the cylinder:
`V_"cylinder" = πr^2h`
Volume of the hemisphere:
`V_"hemisphere" = 2/3 πr^2`
Total capacity of the vessel:
Capacity = `V_"cylinder" - V_"hemisphere"`
Capacity = `πr^2h - 2/3 πr^3`
Simplifying the expression:
Take `1/3 πr^2` out as a common factor:
Capacity = `1/3 πr^2 (3h - 2r)`
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