From a cubical block of wood of side $1 \, m$,a cylinder of the largest possible volume is carved out. The volume (in $m^3$) of the remaining wood 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 $...... cm^3$. $\left[\pi=\frac{22}{7}\right]$

The edge of an ice cube is $14 \, cm$. The volume of the largest cylindrical ice cube that can be formed out of it is.......$cm^3$

$A$ cube of lead with edges measuring $6\, cm$ each is melted and recasted into $27$ equal cubes. The length of the edge of the new cube is.......$cm$

If three metallic spheres of radii $6\, cm$,$8\, cm$,and $10\, cm$ are melted to form a single sphere,the diameter of the new sphere will be (in $cm$)?

$A$ prism with a right triangular base is $25\, cm$ high. If the shorter sides of the triangle are in the ratio of $1: 2$ and the volume of the prism is $100\, cm^3$, what is the length of the longest side of the triangle?