A solid cone of radius $5\mathrm{cm}$ and height $8\mathrm{cm}$ is melted and into small sphere of radius $0.5\mathrm{cm}.$ Find the number of sphere formed.

The total area of a solid metallic sphere is $1256{\mathrm{cm}}^2.$ It is melted and recast into solid right circular cones of radius $2.5\mathrm{cm}$ and height $8\mathrm{cm}.$ Calculate:

The radius of the solid sphere.

The total area of a solid metallic sphere is $1256{\mathrm{cm}}^2.$ It is melted and recast into solid right circular cones of radius $2.5\mathrm{cm}$ and height $8\mathrm{cm}.$ Calculate:

The number of cones recast.

A solid metallic cone, with radius $6\mathrm{cm}$ and height $10\mathrm{cm},$ is made of some heavy metal $A\mathit{.}$ In order to reduce its weight, a conical hole is made in the the cone as shown and it is completely filled with a lighter metal $B\mathit{.}$ The conical hole has a diameter of $6\mathrm{cm}$ and depth $4\mathrm{cm}.$ Calculate the ratio of the volume of metal $A$ to the volume of the metal $B$ in the solid.

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 $\mathrm{\pi }=\frac{22}{7}$)