$A$ building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41 \frac{19}{21} \, m^3$ of air. If the internal diameter of the dome is equal to its total height above the floor,find the height of the building? (in $m$)

The radii of a frustum of a cone are $35 \, cm$ and $21 \, cm$ and its height is $48 \, cm$. Find the curved surface area,the total surface area,and the volume of the frustum of a cone.

Which of the following correctly matches the information given in Part $I$ and Part $II$?

Part $I$	Part $II$
$1.$ $CSA$ of a cylinder	$a.$ $3\pi r^2$
$2.$ $CSA$ of a sphere	$b.$ $2\pi rh$
$3.$ $CSA$ of a cone	$c.$ $4\pi r^2$
$4.$ $TSA$ of a hemisphere	$d.$ $\pi rl$

$A$ container is made by closing one end of a cylinder with radius $35 \,cm$ and height $52 \,cm$ by a cone with height $12 \,cm$. How many litres of water can it store? Find the total surface area of this closed container.

$A$ pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins,respectively. The dimensions of the cuboid are $10 \, cm$,$5 \, cm$,and $4 \, cm$. The radius of each of the conical depressions is $0.5 \, cm$ and the depth is $2.1 \, cm$. The edge of the cubical depression is $3 \, cm$. Find the volume of the wood in the entire stand. (in $, cm^3$)

The base of a cone with radius $21 \, cm$ and height $20 \, cm$ is hemispherical. Find its curved surface area and volume.