$A$ 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 $\pi = \frac{22}{7}$]

Rasheed got a playing top $(lattu)$ as his birthday present,which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere (see figure). The entire top is $5 \, cm$ in height and the diameter of the top is $3.5 \, cm$. Find the area he has to colour (in $cm^2$). (Take $\pi = \frac{22}{7}$)

Two identical cubes each of volume $64 \, cm^{3}$ are joined together end to end. What is the surface area of the resulting cuboid? (in $cm^{2}$)

The radii of the ends of a frustum of a cone $45\, cm$ high are $28\, cm$ and $7\, cm$ (see figure). Find its volume,the curved surface area,and the total surface area (Take $\pi=\frac{22}{7}$).

$A$ factory manufactures $120000$ pencils daily. The pencils are cylindrical in shape,each of length $25 \,cm$ and circumference of base $1.5 \,cm$. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at $\operatorname{Rs.} 0.05$ per $dm^2$ (in $Rs.$).

Write 'True' or 'False' and justify your answer:
The curved surface area of a frustum of a cone is $\pi l(r_{1}+r_{2})$,where $l = \sqrt{h^{2}+(r_{1}+r_{2})^{2}}$,$r_{1}$ and $r_{2}$ are the radii of the two ends of the frustum,and $h$ is the vertical height.