A solid is hemispherical at the bottom and co | vedclass

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

Question

(D) Let the radius of the base be $r$ units and the height of the cone be $h$ units.The surface area of the hemispherical part is $2 \pi r^2$.The curv

Vedclass · Accepted Answer

$1: \sqrt{3}$

Vedclass · Answer

(D) Let the radius of the base be $r$ units and the height of the cone be $h$ units.The surface area of the hemispherical part is $2 \pi r^2$.The curved surface area of the conical part is $\pi r l$,where $l = \sqrt{r^2 + h^2}$ is the slant height.According to the problem,the surface areas of the two parts are equal:$2 \pi r^2 = \pi r \sqrt{r^2 + h^2}$Dividing both sides by $\pi r$ (assuming $r 
eq 0$):$2r = \sqrt{r^2 + h^2}$Squaring both sides:$4r^2 = r^2 + h^2$$3r^2 = h^2$Taking the square root of both sides:$\sqrt{3}r = h$Therefore,the ratio of the radius to the height is:$\frac{r}{h} = \frac{1}{\sqrt{3}}$,which is $1: \sqrt{3}$.

$A$ solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal,then the ratio of the radius and height of its conical part is

Similar Questions

$A$ hollow sphere of internal and external diameters $4\,cm$ and $8\,cm$ respectively is melted into a cone of base diameter $8\,cm$. The height of the cone is......$cm$.

$A$ circular wire of radius $42 \, cm$ is cut and bent in the form of a rectangle whose sides are in the ratio $6:5$. Find the smaller side of the rectangle (in $cm$).

Water is flowing at the rate of $5 \text{ km/h}$ through a pipe of diameter $14 \text{ cm}$ into a rectangular tank which is $50 \text{ m}$ long and $44 \text{ m}$ wide. The time taken,in hours,for the rise in the level of water in the tank to be $7 \text{ cm}$ is:

The diameter of a sphere is $6 \, cm$. It is melted and drawn into a wire of diameter $0.2 \, cm$. Find the length of the wire in meters $(m)$.

$A$ 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

Vedclass Test Series

Exam Paper Generator

Online Exam Module