The radius of the base of a solid cylinder is | vedclass

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

Question

(C) The volume of a cylinder is given by the formula $V_{	ext{cylinder}} = \pi r^2 h$,where $r$ is the radius and $h$ is the height.Given,$h = 3 	ex

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(C) The volume of a cylinder is given by the formula $V_{	ext{cylinder}} = \pi r^2 h$,where $r$ is the radius and $h$ is the height.Given,$h = 3 	ext{ cm}$,so $V_{	ext{cylinder}} = \pi r^2 (3) = 3 \pi r^2 	ext{ cm}^3$.The volume of a cone is given by the formula $V_{	ext{cone}} = \frac{1}{3} \pi r^2 H$,where $H$ is the height of the cone.Since the cylinder is recast into a cone of the same radius,their volumes must be equal.Therefore,$3 \pi r^2 = \frac{1}{3} \pi r^2 H$.Dividing both sides by $\pi r^2$,we get $3 = \frac{1}{3} H$.Multiplying by $3$,we find $H = 9 	ext{ cm}$.

The radius of the base of a solid cylinder is $r \text{ cm}$ and its height is $3 \text{ cm}$. It is recast into a cone of the same radius. The height of the cone will be (in $\text{cm}$):

Similar Questions

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

$A$ cube of lead with edges measuring $6\, cm$ each is melted and recasted into $27$ equal cubes. The length of the edge of the new cube is.......$cm$

Find the length of the canvas $2 \ m$ in width required to make a conical tent $12 \ m$ in diameter and $6.3 \ m$ in slant height (in $m$).

The capacity of a cylindrical tank is $246.4$ litres. If the height is $4$ metres,what is the diameter of the base? (in $m$)

$A$ cone,a hemisphere,and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module