A right cylinder and a right circular cone ha | vedclass

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

Question

(D) Let the radius of both the cylinder and the cone be $r$.Let the height of the cylinder be $h$ and the height of the cone be $H$.The volume of a cy

Vedclass · Accepted Answer

$1:3$

Vedclass · Answer

(D) Let the radius of both the cylinder and the cone be $r$.Let the height of the cylinder be $h$ and the height of the cone be $H$.The volume of a cylinder is given by $V_{cylinder} = \pi r^{2} h$.The volume of a right circular cone is given by $V_{cone} = \frac{1}{3} \pi r^{2} H$.According to the problem,the volumes are equal,so:$\pi r^{2} h = \frac{1}{3} \pi r^{2} H$Dividing both sides by $\pi r^{2}$,we get:$h = \frac{1}{3} H$Therefore,the ratio of the height of the cylinder to the height of the cone is:$\frac{h}{H} = \frac{1}{3} = 1:3$.

$A$ right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is

Similar Questions

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........$cm^2$.

Find out the cost of the log of wood measuring $15 \frac{1}{2} \text{ m}$ by $2 \frac{3}{4} \text{ m}$ by $1 \frac{1}{3} \text{ m}$ at ₹ $45$ per $\text{cm}^3$ (in ₹).

The total number of spherical bullets,each of diameter $5$ decimetre,that can be made by utilizing the maximum of a rectangular block of lead with $11$ $m$ length,$10$ $m$ breadth and $5$ $m$ width is (assume that $\pi > 3$)

$A$ cylindrical bucket is $72\, cm$ high and $28\, cm$ in diameter and is full of water. This water is emptied into a rectangular tank whose length and breadth are $66\, cm$ and $28\, cm$,respectively. What will be the height of the water level in the tank? (in $cm$)

The radii of two cylinders are in the ratio $2:3$. The ratio of their heights is $5:3$. The ratio of their volumes is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module