$A$ rectangular block of metal has dimensions $21\, cm$, $77\, cm$, and $24\, cm$. The block is melted into a sphere. The radius of the sphere is .......... $cm$. (Take $\pi = \frac{22}{7}$)

$A$ rectangular water tank is $80 \, m \times 40 \, m$. Water flows into it through a pipe with an opening area of $40 \, cm^2$ at a speed of $10 \, km/h$. By how much will the water level in the tank rise in half an hour (in $cm$)?

$A$ solid right circular cone of radius $4\, cm$ and height $7\, cm$ is placed inside a cylindrical vessel of radius $5\, cm$ and height $8\, cm$. How much water (in $cm^3$) will be required to fill the cylindrical vessel completely?

$A$ $12\,m$ deep well with internal diameter $3.5\,m$ is dug. The earth taken out from it is spread evenly to form a platform of dimensions $10.5\,m \times 8.8\,m$. Determine the height of the platform in meters. (in $.25$)

$A$ cone of height $9 \, cm$ with diameter of its base $18 \, cm$ is carved out from a wooden solid sphere of radius $9 \, cm$. The percentage of the wood wasted is

$A$ conical cup is filled with ice cream. The ice cream forms a hemispherical shape on its open top. The radius of the hemispherical part is $7 \, cm$. The radius of the hemispherical part equals the height of the cone. Then the volume of the ice cream is $...... cm^3$. $\left[\pi=\frac{22}{7}\right]$