There is a wooden sphere of radius $6 \sqrt{3} \text{ cm}$. The surface area of the largest possible cube cut out from the sphere will be:

The areas of three consecutive faces of a cuboid are $12 \, cm^2$,$20 \, cm^2$,and $15 \, cm^2$. Then the volume (in $cm^3$) of the cuboid is:

The volumes of a right circular cylinder and a sphere are equal. The radius of the cylinder and the diameter of the sphere are equal. The ratio of the height to the radius of the cylinder is:

$A$ 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 $c.c.$)

The height and base radius of a cone are each increased by $100 \%$. The volume of the cone now becomes

Marbles of diameter $1.4\, cm$ are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is $7\, cm.$ Find how many marbles have been dropped in it if the water rises by $5.6\, cm.$