The diameter of a solid hemisphere is $21 \, cm$,then its volume is $\ldots \ldots \ldots \, cm^3$.

The curved surface area of a cone is $550 \, cm^2$. If the radius of the cone is $7 \, cm$,find its volume in $cm^3$.

The volume of a cube is $3375\, cm^{3}$. Find its edge and total surface area.

The radii of three metal spheres are $3 \,cm, 4 \,cm$ and $5 \,cm$ respectively. They are melted into a single solid sphere. Find the radius of the new solid sphere (in $cm$).

Write True or False and justify your answer in each of the following: If a sphere is inscribed in a cube,then the ratio of the volume of the cube to the volume of the sphere will be $6: \pi$.

The surface area and volume of a cube with an edge length of $x \ cm$ are numerically equal. Find the value of $x$.