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10 cards from this deck
V=ฯโซab[y(x)]2โdxV = \pi \int_a^b [y(x)]^2 \, dxV=ฯโซabโ[y(x)]2dx
V=ฯโซab[x(y)]2โdyV = \pi \int_a^b [x(y)]^2 \, dyV=ฯโซabโ[x(y)]2dy
Squared radius multiplied by ฯ\piฯ
Region bounded by y=f(x)y=f(x)y=f(x), x-axis, vertical lines x=ax=ax=a, x=bx=bx=b
Region bounded by x=g(y)x=g(y)x=g(y), y-axis, horizontal lines y=ay=ay=a, y=by=by=b
Square it
V=ฯr2hV = \pi r^2 hV=ฯr2h
Vcomposite=VouterโVinnerV_{\text{composite}} = V_{\text{outer}} - V_{\text{inner}}Vcompositeโ=VouterโโVinnerโ
In exact terms with ฯ\piฯ
The axis of rotation
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