The volume of a solid cylinder whose base dia | vedclass

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

Question

(B) The volume of a cylinder is given by $V = \pi r^2 h$.Let the initial radius be $r_1$ and height be $h_1$. Then $V_1 = \pi r_1^2 h_1 = 3850\, mm^3$

Vedclass · Accepted Answer

$1925$

Vedclass · Answer

(B) The volume of a cylinder is given by $V = \pi r^2 h$.Let the initial radius be $r_1$ and height be $h_1$. Then $V_1 = \pi r_1^2 h_1 = 3850\, mm^3$.For the new cylinder,the length is doubled $(h_2 = 2h_1)$ and the diameter is halved,which means the radius is also halved $(r_2 = r_1 / 2)$.The new volume $V_2$ is given by $V_2 = \pi r_2^2 h_2$.Substituting the new values: $V_2 = \pi (r_1 / 2)^2 (2h_1) = \pi (r_1^2 / 4) (2h_1) = \frac{1}{2} \pi r_1^2 h_1$.Since $V_1 = \pi r_1^2 h_1 = 3850$,we have $V_2 = \frac{1}{2} 	imes 3850 = 1925\, mm^3$.

The volume of a solid cylinder whose base diameter is $14\, mm$ and length is $25\, mm$ is $3850\, mm^3$. If the length of the cylinder is doubled but the diameter is halved,what will be the volume of the resulting cylinder? (in $mm^3$)

Similar Questions

The ratio of total surface area to lateral surface area of a cylinder whose radius is $80 \text{ cm}$ and height $20 \text{ cm}$ is: (in $:1$)

$A$ well of $11.2 \, m$ diameter is dug $8 \, m$ deep. The earth taken out has been spread all around it to a width of $7 \, m$ to form a circular embankment. Find the height of the embankment in meters.

The radii of two cones are in the ratio $2:1,$ and their volumes are equal. Find the ratio of their heights.

$A$ right circular cone is $3.6 \ cm$ high and the radius of its base is $1.6 \ cm$. It is melted and recast into a right circular cone with a base radius of $1.2 \ cm$. The height of the new cone (in $cm$) is:

If the radius of a sphere is increased by $2 \, m$,its surface area is increased by $704 \, m^2$. What is the radius of the original sphere? (in $m$)
(use $\pi = \frac{22}{7}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module