$A$ cylinder is closed at both the ends by hemispheres. The radius of the cylinder is $7 \, cm$ and the total height of the article is $34 \, cm$. Find the total surface area of the article. (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 $\pi = 3.14$)

$A$ 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 $, cm^2$)

The radius and the height of a cylinder are $28 \, cm$ and $54.5 \, cm$ respectively. It is closed at one end by a hemisphere and at the other end by a $21 \, cm$ high cone. Find the total surface area of the combined article. (in $cm^2$)

The radii of the top and bottom of a bucket of slant height $45 \, cm$ are $28 \, cm$ and $7 \, cm$,respectively. The curved surface area of the bucket is (in $cm^2$)

Derive the formula for the curved surface area and total surface area of the frustum of a cone.