$A$ 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 $, cm^{3}$)

$A$ solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1\, cm$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

$A$ container,opened from the top and made up of a metal sheet,is in the form of a frustum of a cone of height $16 \, cm$ with radii of its lower and upper ends as $8 \, cm$ and $20 \, cm$,respectively. Find the cost of the milk which can completely fill the container,at the rate of $Rs. \, 20$ per litre. Also,find the cost of the metal sheet used to make the container,if it costs $Rs. \, 8$ per $100 \, cm^2$. (Take $\pi = 3.14$)

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

How many silver coins,$1.75 \,cm$ in diameter and of thickness $2 \,mm$,must be melted to form a cuboid of dimensions $5.5 \,cm \times 10 \,cm \times 3.5 \,cm$? [Take $\pi = \frac{22}{7}$]

$A$ hemispherical tank full of water is emptied by a pipe at the rate of $3 \frac{4}{7}$ $litres$ per $second.$ How much time will it take to empty half the tank,if it is $3 \,m$ in $diameter?$ (in $minutes$) (Take $\pi=\frac{22}{7}$)