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(D) Let the radius of the cylinder be $r$ and the height be $h$.The curved surface area $(CSA)$ of a cylinder is $2\pi rh$.The total surface area $(TS

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$3: 2$

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(D) Let the radius of the cylinder be $r$ and the height be $h$.The curved surface area $(CSA)$ of a cylinder is $2\pi rh$.The total surface area $(TSA)$ of a cylinder is $2\pi rh + 2\pi r^2 = 2\pi r(h + r)$.Given the ratio $CSA : TSA = 2 : 5$,we have:$\frac{2\pi rh}{2\pi r(h + r)} = \frac{2}{5}$$\frac{h}{h + r} = \frac{2}{5}$Cross-multiplying gives $5h = 2(h + r)$.$5h = 2h + 2r$$3h = 2r$Therefore,the ratio of the radius to the height is $\frac{r}{h} = \frac{3}{2}$,which is $3: 2$.

The ratio of the curved surface area and the total surface area of a cylinder is $2: 5$. Find the ratio of the radius and height of the cylinder.

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