The radius of a cylinder is made twice as lar | vedclass

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

Question

(A) Let the original radius be $r$ and the original height be $h$. The original volume $V$ is given by $V = \pi r^2 h$.If the new radius is $R = 2r$ a

Vedclass · Accepted Answer

$1/4$ of original

Vedclass · Answer

(A) Let the original radius be $r$ and the original height be $h$. The original volume $V$ is given by $V = \pi r^2 h$.If the new radius is $R = 2r$ and the new height is $H$,the new volume $V'$ must be equal to $V$.So,$V' = \pi R^2 H = \pi (2r)^2 H = \pi (4r^2) H = 4 \pi r^2 H$.Since $V' = V$,we have $4 \pi r^2 H = \pi r^2 h$.Dividing both sides by $\pi r^2$,we get $4H = h$,which implies $H = \frac{1}{4} h$.Therefore,the height should be $\frac{1}{4}$ of the original height.

The radius of a cylinder is made twice as large. How should the height be changed so that its volume remains unchanged?

Similar Questions

$2$ cubes have volumes in the ratio $1:27$. The ratio of the area of the face of one to that of the other is

$A$ sphere is cut into two hemispheres. One of them is used as a bowl. It takes $8$ bowlfuls of this to fill a conical vessel of height $12\, cm$ and radius $6\, cm$. The radius of the sphere (in centimeter) will be

The diameter and slant height of a conical tomb are $28\, m$ and $50\, m$,respectively. The cost of whitewashing its curved surface at the rate of $80$ paise per $m^2$ is (in $Rs.$):

$5$ persons will live in a tent. If each person requires $16\, m^2$ of floor area and $100\, m^3$ space for air,then the height of the cone of smallest size to accommodate these persons would be? (in $m$)

The radius of a cylinder is increased by $20 \%$,keeping its height unchanged. What is the percentage increase in its volume?

Vedclass Test Series

Exam Paper Generator

Online Exam Module