如图,在长方形ABCD中,长方形ABCD的面积为a^2n+1*b^n3,而BC=2a^n+1*b^n,将长方形卷成纸筒做
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S=a^(2n+1)*b^(n+3)

BC=2a^(n+1)*b^n

∴AB=S/BC=[a^(2n+1)*b^(n+3)]/[2a^(n+1)*b^n]=(a^n*b^3)/2

若以AB为母线L,则2πR=BC=2a^(n+1)*b^n

∴R=[a^(n+1)*b^n]/π

∴V=πR^2*L=π{[a^(n+1)*b^n]/π}^2*(a^n*b^3)/2=[a^(3n+2)*b^(2n+3)]/2π

若以BC为母线L,则2πR=AB=(a^n*b^3)/2

∴R=(a^n*b^3)/4π

∴V=πR^2*L=π[(a^n*b^3)/4π]^2*2a^(n+1)*b^n=[a^(3n+1)*b^(n+6)]/8π

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