A cylinder and a cone have their heights in t | vedclass

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

Question

(C) Let the heights of the cylinder and cone be $h_1 = 2x$ and $h_2 = 3x$ respectively.Let the radii of the cylinder and cone be $r_1 = 3y$ and $r_2 =

Vedclass · Accepted Answer

$9:8$

Vedclass · Answer

(C) Let the heights of the cylinder and cone be $h_1 = 2x$ and $h_2 = 3x$ respectively.Let the radii of the cylinder and cone be $r_1 = 3y$ and $r_2 = 4y$ respectively.The volume of a cylinder is given by $V_1 = \pi r_1^2 h_1$.The volume of a cone is given by $V_2 = \frac{1}{3} \pi r_2^2 h_2$.The ratio of their volumes is $\frac{V_1}{V_2} = \frac{\pi r_1^2 h_1}{\frac{1}{3} \pi r_2^2 h_2} = \frac{3 r_1^2 h_1}{r_2^2 h_2}$.Substituting the given ratios: $\frac{V_1}{V_2} = \frac{3 	imes (3y)^2 	imes (2x)}{(4y)^2 	imes (3x)} = \frac{3 	imes 9y^2 	imes 2x}{16y^2 	imes 3x} = \frac{54}{48} = \frac{9}{8}$.Thus,the ratio of their volumes is $9:8$.

$A$ cylinder and a cone have their heights in the ratio $2:3$ and the radii of their bases in the ratio $3:4$. Find the ratio of their volumes.

Similar Questions

How many bricks,each measuring $250\, cm$ by $12.5\, cm$ by $7.5\, cm$,will be required to build a $5\, m$ long,$3\, m$ high and $20\, cm$ thick wall?

Volume of the cylinder is $1650\, m^3$,whereas the surface area of its base is $78 \frac{4}{7}\, m^2$. Find out the height of the cylinder (in $m$).

Some bricks are arranged in an area measuring $20 \, m^3$. If the length, breadth, and height of each brick are $25 \, cm$, $12.5 \, cm$, and $8 \, cm$ respectively, then the number of bricks in that pile is (assume there is no gap between two bricks):

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is $5\, cm$,the height of the cone is........$cm$.

$A$ cylinder with base radius of $8\, cm$ and height of $2\, cm$ is melted to form a cone of height $6\, cm.$ The radius of the cone will be (in $cm$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module