X and Y are two cylinders of the same height. | vedclass

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

Question

(C) Let the heights of cylinders $X$ and $Y$ be $h_1 = h_2 = h$.Let the diameter of $X$ be $d_1$ and the diameter of $Y$ be $d_2$. Given $d_1 = \frac{

Vedclass · Accepted Answer

half the volume of $Y$

Vedclass · Answer

(C) Let the heights of cylinders $X$ and $Y$ be $h_1 = h_2 = h$.Let the diameter of $X$ be $d_1$ and the diameter of $Y$ be $d_2$. Given $d_1 = \frac{1}{2} d_2$,which implies $d_2 = 2d_1$.The volume of a cylinder is given by $V = \pi r^2 h = \pi (d/2)^2 h = \frac{\pi d^2 h}{4}$.Volume of $X$ $(V_X)$ = $\frac{\pi d_1^2 h}{4}$.Volume of $Y$ $(V_Y)$ = $\frac{\pi d_2^2 h}{4} = \frac{\pi (2d_1)^2 h}{4} = \frac{4 \pi d_1^2 h}{4} = 4 V_X$.If the height of $X$ is doubled,the new volume $V_X' = \frac{\pi d_1^2 (2h)}{4} = 2 	imes \frac{\pi d_1^2 h}{4} = 2 V_X$.Since $V_Y = 4 V_X$,then $V_X = \frac{1}{4} V_Y$.Therefore,$V_X' = 2 	imes (\frac{1}{4} V_Y) = \frac{1}{2} V_Y$.Thus,the volume of $X$ becomes half the volume of $Y$.

$X$ and $Y$ are two cylinders of the same height. The base of $X$ has a diameter which is equal to half the diameter of the base of $Y$. If the height of $X$ is doubled,the volume of $X$ becomes

Similar Questions

$A$ cone-shaped circular tent is $9 \, m$ high and the circumference of its circular base is $44 \, m$. How much air is contained in the tent? (in $m^3$) (Use $\pi = \frac{22}{7}$)

The base of a right prism is a quadrilateral $ABCD$. Given that $AB = 9\, cm$,$BC = 14\, cm$,$CD = 13\, cm$,$DA = 12\, cm$ and $\angle DAB = 90^{\circ}$. If the volume of the prism is $2070\, cm^3$,then the area of the lateral surface is........$cm^2$.

$A$ field is in the form of a rectangle of length $18\, m$ and width $15\, m$. $A$ pit,$7.5\, m$ long,$6\, m$ broad and $0.8\, m$ deep,is dug in a corner of the field and the earth taken out is evenly spread over the remaining area of the field. The level of the field raised is......$cm$

$A$ $4\, cm$ cube is cut into $1\, cm$ cubes. What is the ratio of the total surface area of all the small cubes to the surface area of the large cube?

$A$ hollow sphere of internal and external diameters $4\,cm$ and $8\,cm$ respectively is melted into a cone of base diameter $8\,cm$. The height of the cone is......$cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module