$A$ metallic right circular cone $20 \, cm$ high and whose vertical angle is $60^{\circ}$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained is drawn into a wire of diameter $\frac{1}{16} \, cm$,find the length of the wire in meters. [Use $\pi = \frac{22}{7}$]

Metallic spheres of radii $6 \, cm$,$8 \, cm$,and $10 \, cm$,respectively,are melted to form a single solid sphere. Find the radius of the resulting sphere (in $cm$).

$A$ copper rod of diameter $1 \,cm$ and length $8 \,cm$ is drawn into a wire of length $18 \,m$ of uniform thickness. Find the thickness of the wire. (in $mm$)

$A$ medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is $14 \, mm$ and the diameter of the capsule is $5 \, mm$. Find its surface area. $\left[ \text{Use } \pi = \frac{22}{7} \right]$ (in $mm^2$)

$A$ $20\, m$ deep well with diameter $7\, m$ is dug and the earth from digging is evenly spread out to form a platform $22\, m$ by $14\, m$. Find the height of the platform. (in $m$) [Take $\pi=\frac{22}{7}$]

$A$ vessel is in the form of an inverted cone. Its height is $8 \, cm$ and the radius of its top,which is open,is $5 \, cm$. It is filled with water up to the brim. When lead shots,each of which is a sphere of radius $0.5 \, cm$,are dropped into the vessel,one-fourth of the water flows out. Find the number of lead shots dropped in the vessel. [Take $\pi = \frac{22}{7}$.]