$A$ metallic sphere of radius $4.2 \, cm$ is melted and recast into the shape of a cylinder of radius $6 \, cm$. Find the height of the cylinder. (in $cm$) [Take $\pi = \frac{22}{7}$]

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

$A$ spherical glass vessel has a cylindrical neck $8 \, cm$ long and $2 \, cm$ in diameter. The diameter of the spherical part is $8.5 \, cm$. By measuring the amount of water it holds,a child finds its volume to be $345 \, cm^{3}$. Check whether she is correct,taking the above as the inside measurements,and $\pi = 3.14$. (in $, cm^{3}$)

Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see figure). If the base of the shed is of dimension $7\,m \times 15\,m,$ and the height of the cuboidal portion is $8\,m,$ find the volume of air that the shed can hold. Further,suppose the machinery in the shed occupies a total space of $300\,m^3,$ and there are $20$ workers,each of whom occupy about $0.08\,m^3$ space on an average. Then,how much air is in the shed? (in $m^3$) (Take $\pi = \frac{22}{7}$)

$A$ juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical glass was $5 \, cm$,but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was $10 \, cm$,find the apparent capacity of the glass and its actual capacity (in $cm^3$). (Use $\pi = 3.14$)

Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end (see figure). The height of the cylinder is $1.45\, m$ and its radius is $30\, cm$. Find the total surface area of the bird-bath in $m^2$. (Take $\pi = \frac{22}{7}$)