The radius of a cylinder is doubled and the h | vedclass

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

Question

(C) Let the initial radius and height of the cylinder be $r$ and $h$,respectively.The initial volume $V_{1}$ is given by the formula $V_{1} = \pi r^{2

Vedclass · Accepted Answer

$2:1$

Vedclass · Answer

(C) Let the initial radius and height of the cylinder be $r$ and $h$,respectively.The initial volume $V_{1}$ is given by the formula $V_{1} = \pi r^{2} h$.According to the problem,the new radius $r' = 2r$ and the new height $h' = \frac{h}{2}$.The new volume $V_{2}$ is given by $V_{2} = \pi (r')^{2} h' = \pi (2r)^{2} \left(\frac{h}{2}\right)$.Simplifying the expression for $V_{2}$,we get $V_{2} = \pi (4r^{2}) \left(\frac{h}{2}\right) = 2 \pi r^{2} h$.The ratio of the new volume to the previous volume is $\frac{V_{2}}{V_{1}} = \frac{2 \pi r^{2} h}{\pi r^{2} h} = \frac{2}{1}$.Therefore,the ratio is $2:1$.

The radius of a cylinder is doubled and the height is halved. What is the ratio between the new volume and the previous volume?

Similar Questions

The height of the right pyramid whose area of the base is $30\, m^{2}$ and volume is $500\, m^{3}$ is ...... $m$.

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

$A$ rectangular sheet of area $264 \text{ cm}^2$ and width $11 \text{ cm}$ is rolled along its breadth to make a hollow cylinder. The volume of the cylinder is (in $\text{cm}^3$):

There is a wooden sphere of radius $6 \sqrt{3} \text{ cm}$. The surface area of the largest possible cube cut out from the sphere will be:

The radius and height of a right circular cone are in the ratio $3: 4$. If its volume is $96\pi\, cm^3$,what is its slant height (in $cm$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module