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(D) Let the radius be $r$ and the height be $h$.Curved Surface Area $(CSA)$ $= 2\pi rh$,Volume $(V) = \pi r^2h$.Given $\frac{2\pi rh}{\pi r^2h} = \fra

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$7:10$

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(D) Let the radius be $r$ and the height be $h$.Curved Surface Area $(CSA)$ $= 2\pi rh$,Volume $(V) = \pi r^2h$.Given $\frac{2\pi rh}{\pi r^2h} = \frac{1}{7} \Rightarrow \frac{2}{r} = \frac{1}{7} \Rightarrow r = 14$.Total Surface Area $(TSA)$ $= 2\pi rh + 2\pi r^2 = 2\pi r(h+r)$.Given $\frac{2\pi r(h+r)}{\pi r^2h} = \frac{187}{770}$.Substitute $r = 14$:$\frac{2(h+14)}{14h} = \frac{187}{770} \Rightarrow \frac{h+14}{7h} = \frac{187}{770}$.$\frac{h+14}{7h} = \frac{17}{70} \Rightarrow 10(h+14) = 17h$.$10h + 140 = 17h \Rightarrow 7h = 140 \Rightarrow h = 20$.The ratio of radius to height is $r:h = 14:20 = 7:10$.

The ratio of the curved surface area and volume of a cylinder is $1:7$. The ratio of the total surface area and volume is $187:770$. What is the ratio of its base radius to its height?

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