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Definite integrals, areas and volumes

Definite integrals, areas and volumes · Diagrams

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Recognise cylinders and full cones

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Rectangles rotated about either axis produce cylinders with volume pi r squared h. The two triangular regions drawn with an apex on the axis produce full cones with volume one third pi r squared h; a nonzero radius at both ends would instead give a frustum.
Rectangles rotated about either axis produce cylinders with volume pi r squared h. The two triangular regions drawn with an apex on the axis produce full cones with volume one third pi r squared h; a nonzero radius at both ends would instead give a frustum.
Rectangles rotated about either axis produce cylinders with volume pi r squared h. The two triangular regions drawn with an apex on the axis produce full cones with volume one third pi r squared h; a nonzero radius at both ends would instead give a frustum.
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