Problem

The filled right triangle with vertices \((0,~0)\), \((0,~h)\), and \((r,~0)\) rotates \(360°\) about \(x~=~0\). Use the diagram to state the region, axis, resulting solid, radius, height, slant height, and volume.

Prompt diagram for M3-037-A11-V02: the generating region, rotation axis, dimensions, and 360-degree sweep with the resulting solid withheld.

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The generating region is the filled triangle, the axis is x = 0, the solid is a right circular cylinder of radius r, height h, and volume pi r² h.

The generating region is treated as only its boundary, the axis is x = 0, the result is a hollow conical surface of radius r, height h, slant height sqrt(r²+h²), and enclosed volume 0.

The generating region is the filled triangle, the axis is x = 0, the solid is a right circular cone of radius r, height h, slant height sqrt(r²+h²), and volume (1/3)pi r² h.

The generating region is the filled triangle, the axis is x = 0, the solid is a right circular cone of radius h, height r, slant height sqrt(r²+h²), and volume (1/3)pi h² r.

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The filled right triangle with vertices \((0,~0)\), \((0,~h)\), and \((r,~0)\) rotates \(360°\) about \(x~=~0\). Use the diagram to state the region, axis, resulting solid, radius, height, slant height, and volume.

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