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Name of solid geometric figure

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What is the English name of this solid geometric figure?

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I have yet to find the correct English term for it. In Danish it is "kugleudsnit".

Bonus question: How could this be derived without using integration, but knowing formulas for volume of cylinder, sphere and cone?

geometry terminology euclidean-geometry solid-geometry
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A spherical cone seems to be what you're looking for.

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Wikipedia lists it as a spherical sector and Wolfram as a spherical cone.

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