A hollow sphere of internal and external radii $6\mathrm{cm}$ and $8\mathrm{cm}$ respectively is melted and recast into small cones of base radius $2\mathrm{cm}$ and height $8\mathrm{cm}.$ Find the number of cones.

The surface area of a solid metallic sphere is $2464{\mathrm{cm}}^2.$ It is melted and recast into solid right circular cones of radius $3.5\mathrm{cm}$ and height $7\mathrm{cm}.$ Calculate:

The radius of the sphere.

(Take $\mathrm{\pi }=\frac{22}{7}$)

The surface area of a solid metallic sphere is $2464{\mathrm{cm}}^2.$ It is melted and recast into solid right circular cones of radius $3.5\mathrm{cm}$ and height $7\mathrm{cm}.$ Calculate:

The number of cones recast.

(Take $\mathrm{\pi }=\frac{22}{7}$)

From a rectangular solid of metal $42\mathrm{cm}$ by $30\mathrm{cm}$ by $20\mathrm{cm},$ a conical cavity of diameter $14\mathrm{cm}$ and depth $24\mathrm{cm}$ is drilled out. Find:

The surface area of remaining solid.

From a rectangular solid of metal $42\mathrm{cm}$ by $30\mathrm{cm}$ by $20\mathrm{cm},$ a conical cavity of diameter $14\mathrm{cm}$ and depth $24\mathrm{cm}$ is drilled out. Find:

The volume of remaining solid.

$\left(\mathrm{\pi }=\frac{22}{7}\right)$

From a rectangular solid of metal $42\mathrm{cm}$ by $30\mathrm{cm}$ by $20\mathrm{cm},$ a conical cavity of diameter $14\mathrm{cm}$ and depth $24\mathrm{cm}$ is drilled out. Find:

The weight of the material drilled out if it weighs $7\mathrm{gm} \mathrm{per} {\mathrm{cm}}^3.$