$A$ solid cone is $25 \ cm$ high and the radius of its base is $50 \ cm$. It is melted and recast into a solid sphere. Determine the surface area of the sphere (in $cm^2$).

$A$ right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is $343 \, c.c.$,then what approximately is the volume of the cone? (in $c.c.$)

$3$ equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes.

$A$ 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

$A$ $1 \, m^3$ of metal weighing $90 \, Kg$ is rolled into a square bar $9 \, m$ long. An exact cube is cut off from the bar. How much does it weigh? (in $kg$)

$A$ solid cone of height $24 \, cm$ and base radius $8 \, cm$ is melted to form a solid cylinder of radius $6 \, cm$ and height $6 \, cm$. In the whole process,what percent of material is wasted (in $\%$)?