Conversion of Solid from One Shape to Another

The radius and height of a conical vessel are $10 \mathrm{cm}$ and $18 \mathrm{cm}$, respectively, which is filled with water to the brim. It is poured into a cylindrical vessel of radius $5 \mathrm{cm}$. Find the height of the water level in the cylindrical vessel in $\mathrm{cm}$.

A $20 \mathrm{m}$ deep well with diameter $7 \mathrm{m}$ is dug and the earth from digging is evenly spread out to form a platform $22$ $\mathrm{m}\times 14$ $\mathrm{m}$. Find the height of platform in $\mathrm{m}$.

The diameter of a metallic sphere is $6 \mathrm{cm}$. It is melted and drawn into a wire of length $36 \mathrm{m}$ and of uniform circular cross-section. Find its radius in $\mathrm{mm}$.

A conical vessel has radius $10 \mathrm{cm}$ and height $18 \mathrm{cm}$ and is completely filled with water which is transferred in a cylindrical vessel of radius $5 \mathrm{cm}$. Find the level of water (height) in cylindrical vessel in $\mathrm{cm}$.

Three solid metallic spheres of radii $6 \mathrm{cm}$, $8 \mathrm{cm}$ and $10 \mathrm{cm}$, respectively are melted and then recast into a big sphere. Find the radius of this sphere in $\mathrm{cm}$.

A metallic sphere of radius $9 \mathrm{cm}$ is melted and then recast into small cones of radius $3 \mathrm{cm}$ and height $6 \mathrm{cm}$. Find the number of cones thus formed.

A candle of diameter $2.8 \mathrm{cm}$ is formed from a cuboid of dimensions $11 \mathrm{cm}\times 3.5 \mathrm{cm}\times 2.5 \mathrm{cm}$. Find the length of the candle in $\mathrm{cm}$.

A hemispherical bowl of internal radius $9 \mathrm{cm}$ is full of liquid. This liquid is to be filled into cylindrical shaped small bottles each of diameter $3 \mathrm{cm}$ and height $4 \mathrm{cm}$. How many bottles are necessary to empty the bowl?

A sphere of $6 \mathrm{cm}$ diameter is dropped into a cylindrical vessel of diameter $12 \mathrm{cm}$. Find the rise in water level in the vessel.

The dimensions of a solid rectangular slab of lead are $66 \mathrm{cm}$, $42 \mathrm{cm}$ and $21 \mathrm{cm}$ respectively. By melting this, how many spheres of diameter $4.2 \mathrm{cm}$ can be formed? 

How many cones of $3 \mathrm{cm}$ radius and $6 \mathrm{cm}$ height, are formed by melting a metallic sphere of radius $9 \mathrm{cm}$?

A cylinder is made of lead whose radius is $4 \mathrm{cm}$ and height is $10 \mathrm{cm}$. By melting this, how many spheres of radius $2 \mathrm{cm}$ can be formed?

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of cylinder is $5 \mathrm{cm}$, then height of the cone is