$A$ solid consisting of a right circular cone of height $120\, cm$ and radius $60\, cm$ standing on a hemisphere of radius $60\, cm$ 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 $60\, cm$ and its height is $180\, cm$. [Take $\pi = \frac{22}{7}$.] (in $m^3$)

$A$ wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in the figure. The height of the entire rocket is $26\, cm,$ while the height of the conical part is $6\, cm.$ The base of the conical portion has a diameter of $5\, cm,$ while the base diameter of the cylindrical portion is $3\, cm.$ If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (in $cm^2$) (Take $\pi=3.14$)

$A$ drinking glass is in the shape of a frustum of a cone of height $14 \, cm$. The diameters of its two circular ends are $4 \, cm$ and $2 \, cm$. Find the capacity of the glass. [Use $\pi = \frac{22}{7}$]

Rachel,an engineering student,was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is $3\, cm$ and its total length is $12\, cm$. If each cone has a height of $2\, cm$,find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.) Unless stated otherwise,take $\pi = \frac{22}{7}$. (in $cm^3$)

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 $cm$).

$2$ cubes each of volume $64 \, cm^3$ are joined end to end. Find the surface area of the resulting cuboid in $cm^2$.