A cylinder,a hemisphere,and a cone stand on t | vedclass

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(C) Let the common radius be $r$ and the common height be $h$. Since they stand on the same base and have the same height,for the hemisphere,$h = r$.T

Vedclass · Accepted Answer

$3: 2: 1, \sqrt{2}: \sqrt{2}: 1$

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(C) Let the common radius be $r$ and the common height be $h$. Since they stand on the same base and have the same height,for the hemisphere,$h = r$.Thus,$h = r$ for all three shapes.$1$. Ratio of volumes:$V_{cylinder} = \pi r^2 h = \pi r^3$$V_{hemisphere} = \frac{2}{3} \pi r^3$$V_{cone} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi r^3$Ratio $= \pi r^3 : \frac{2}{3} \pi r^3 : \frac{1}{3} \pi r^3 = 1 : \frac{2}{3} : \frac{1}{3} = 3 : 2 : 1$.$2$. Ratio of curved surface areas $(CSA)$:$CSA_{cylinder} = 2 \pi r h = 2 \pi r^2$$CSA_{hemisphere} = 2 \pi r^2$$CSA_{cone} = \pi r l = \pi r \sqrt{r^2 + h^2} = \pi r \sqrt{r^2 + r^2} = \pi r^2 \sqrt{2}$Ratio $= 2 \pi r^2 : 2 \pi r^2 : \sqrt{2} \pi r^2 = 2 : 2 : \sqrt{2} = \sqrt{2} : \sqrt{2} : 1$.

$A$ cylinder,a hemisphere,and a cone stand on the same base and have the same heights. Find the ratio of their volumes and also the ratio of the areas of their curved surfaces.

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