A solid consisting of a right circular cone of height $120 \mathrm{c}\mathrm{m}$ and radius $60 \mathrm{c}\mathrm{m}$ standing on a hemisphere of radius $60 \mathrm{c}\mathrm{m}$ is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is $60 \mathrm{c}\mathrm{m}$ and its height is $180 \mathrm{c}\mathrm{m}$.

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is $21 \mathrm{cm}$ and its volume is $\frac{2}{3}$ of the volume of the hemisphere, calculate the height of the cone and surface area of the toy.

The diameter of a metallic sphere is $6 \mathrm{cm}$. The sphere is melted and drawn into a wire of uniform circular cross-section. if the length of the wire is $36 m$, find its radius.

Three metallic solid cubes whose edges are $3 \mathrm{cm}, 4 \mathrm{cm}$ and $5 \mathrm{cm}$ are melted and formed into a single cube. Find the edge of the cube so formed.

A solid metallic sphere of diameter $8 cm$ is melted and drawn into a cylindrical wire of uniform width . If the length of the wire is 12m, find its width.

The dimension of a solid iron cuboid are $4.4m \times 2.6 m \times 1.0 m.$ It is melted and recast into a hollow cylindrical pipe of $30 cm$inner radius and thickness $5 m.$ Find the length of the pipe.