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in Surface Areas And Volumes by (46.2k points)
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The magnitude of the volume of a closed right circular cylinder of unit height divided by the magnitude of the total surface area of the cylinder (r being the radius of the cylinder) is equal to

(a) \(\frac12\bigg(1+\frac1r\bigg)\)

(b) \(\frac12\bigg(1+\frac1{r+1}\bigg)\)

(c) \(\frac12\bigg(1-\frac1r\bigg)\)

(d) \(\frac12\bigg(1-\frac1{r+1}\bigg)\)

1 Answer

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Best answer

(d) \(\frac12\bigg(1-\frac1{r+1}\bigg)\)

Required magnitude = \(\frac{\text{Volume of cylinder}}{\text{Total surface area of cylinder}}\)

\(\frac{πr^2h}{2πr(h+r)}=\frac{πr^2}{2πr(1+r)}\)         (∵ h = 1)

\(\frac12\frac{r}{(1+r)} =\) \(\frac12\bigg(1-\frac1{r+1}\bigg)\)

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