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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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.

Similar Questions

$A$ reservoir, $30\, m$ long and $15\, m$ broad, is filled with water. How many gallons of water must be taken out to lower the level of water by $4\, m$? (in gallons)

$A$ rectangular tank is $30\,m$ long and $20\,m$ broad. Water is being flown into it through a square pipe of side $5\,cm$. What is the speed of water if the level of water in the tank rises by $1\,m$ in $8\,hours$? (in $km/h$)

Three cubes with sides in the ratio $3:4:5$ are melted to form a single cube whose diagonal is $12\sqrt{3} \text{ cm}$. The sides of the cubes are

From a cubical block of wood of side $1 \, m$,a cylinder of the largest possible volume is carved out. The volume (in $m^3$) of the remaining wood is

$66 \text{ cm}^3$ of silver is drawn into a wire $1 \text{ mm}$ in diameter. The length of the wire in metres will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module