MCQ
A metallic solid sphere of radius $9\ cm$ is melted to form a solid linder of radius $9\ cm$. The height of the cylin er is :
- ✓$12\ cm$
- B$18\ cm$
- C$36\ cm$
- D$96\ cm$
✓
Answer
Correct option: A.
$12\ cm$
The metallic solid sphere is melted to from a solid cylinder.
Let the height of the cylinder be $h$.
So, volume of the sphere $=$ volume of the cylinder
$\Rightarrow\frac{4}{3}\pi\text{r}_1^3=\pi\text{r}^2\text{h}$
$\Rightarrow\frac{4}{3}\text{r}_1=\text{h}$
$\Rightarrow\text{h}=\frac{4}{3}\times9=12\text{ cm}$
Let the height of the cylinder be $h$.
So, volume of the sphere $=$ volume of the cylinder
$\Rightarrow\frac{4}{3}\pi\text{r}_1^3=\pi\text{r}^2\text{h}$
$\Rightarrow\frac{4}{3}\text{r}_1=\text{h}$
$\Rightarrow\text{h}=\frac{4}{3}\times9=12\text{ cm}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The smallest rational number by which $\frac{1}{3}$ should be multiplied so that its decimal expansion terminates after one place of decimal, is:
→The value of $'k\ ’$ so that the system of linear equations $kx - y - 2 = 0$ and $6x - 2y - 3 = 0$ have no solution is :
→In the adjoining figure, if $P C$ is the tangent at $A$ of the circle with $\angle P A B$ $=72^{\circ}$ and $\angle A O B=132^{\circ}$, then $\angle A B C=$
→If the equation $x^2- ax + 1 = 0$ has two distinct roots, then :
→For some integer m, every even integer is of the form:
If $\theta$ is an acute angle such that $\sec^2\theta=3,$ then the value of $\frac{\tan^2\theta-\text{cosec}^2\theta}{\tan^2\theta+\text{cosec}^2\theta}$ is:
→26. If 2 is a root of the equation $x^2+b x+12=0$ and the equation $x^2+b x+q=0$ has equal roots, then $q=$
→The coordinates of the fourth vertex of the rectangle formed by the points $O(0,0), A(2,0)$ and $B(0,3)$ are
→In an $A.P$. if $S_n= 3n^2+ 2n,$ then the value of $d$ is :
→If $\theta$ is an acute angle such that $\sec^2\theta=3,$ then the value of $\frac{\tan^2\theta-\text{cosec}^2\theta}{\tan^2\theta+\text{cosec}^2\theta}$ is :
→