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 $\text{cm}$):

$A$ solid sphere of radius $1 \, cm$ is melted to convert into a wire of length $100 \, cm$. The radius of the wire (using $\sqrt{3} = 1.732$) is ......... $cm$.

$A$ cylinder with base radius $8\, cm$ and height $2\, cm$ is melted to form a cone of height $6\, cm$. The radius of the cone will be (in $cm$):

$2\, cm$ of rain has fallen on a $1\, km^2$ of land. Assuming that $50\%$ of the raindrops could have been collected and contained in a pool having a $100\, m \times 10\, m$ base,by what level would the water level in the pool have increased? (in $m$)

The base of a right prism is an equilateral triangle. If the lateral surface area and volume are $120 \, cm^2$ and $40 \sqrt{3} \, cm^3$,respectively,then the side of the base of the prism is ...... $cm$.

The sum of the radius of the base and the height of a solid cylinder is $37\, m$. If the total surface area of the solid cylinder is $1628\, m^2$,then the circumference of its base and the volume of the cylinder are: