$A$ vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14 \, cm$ and the total height of the vessel is $13 \, cm$. Find the inner surface area of the vessel. [Use $\pi = \frac{22}{7}$] (in $, cm^2$)

$A$ 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 $\pi = 3.14$)

$A$ cylindrical bucket,$32 \, cm$ high and with a base radius of $18 \, cm$,is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \, cm$,find the radius and slant height of the heap. [Take $\pi = \frac{22}{7}$]

$A$ wooden article was made by scooping out a hemisphere from each end of a solid cylinder,as shown in the figure. If the height of the cylinder is $10 \, cm$ and its base radius is $3.5 \, cm$,find the total surface area of the article (in $cm^2$).

$A$ gulab jamun contains sugar syrup up to about $30\%$ of its volume. Find approximately how much syrup would be found in $45$ gulab jamuns,each shaped like a cylinder with two hemispherical ends with length $5\,cm$ and diameter $2.8\,cm$ (see figure) (in $cm^3$) [take $\pi=\frac{22}{7}$].

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