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

$1496 \, cm^3$ of a metal is used to cast a pipe of length $28 \, cm$. If the internal radius of the pipe is $8 \, cm$,then the outer radius of the pipe is (in $cm$):

$A$ solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is $h$. If the total volume of the solid is three times the volume of the cone,then the height of the cylinder is

The cost of paint is ₹ $36/kg$. If $1\, kg$ of paint covers $1.5\, m^2$,how much will it cost to paint the outside of a cube having a $2.5\, m$ side?

Assume that a drop of water is spherical and its diameter is $\frac{1}{10} \text{ cm}$. $A$ conical glass has a height equal to the diameter of its rim. If $32,000$ drops of water fill the glass completely,then the height of the glass (in $\text{cm}$) is:

The diameter of a copper sphere is $18 \, cm$. The sphere is melted and drawn into a long wire of uniform circular cross-section. If the length of the wire is $108 \, m$,the diameter of the wire is ....... $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module