Write 'True' or 'False' and justify your answer:
Two identical solid hemispheres of equal base radius $r \text{ cm}$ are joined together along their bases. The total surface area of the resulting solid is $6 \pi r^{2}$.

$A$ cylinder is closed at both ends by hemispheres. The radius of the cylinder is $21 \, cm$ and the total height of the article is $92 \, cm$. Find the total surface area of the article (in $cm^2$).

$A$ 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 $, cm^3$)

$A$ wall $24 \, m$ long,$0.4 \, m$ thick and $6 \, m$ high is constructed with bricks each of dimensions $25 \, cm \times 16 \, cm \times 10 \, cm$. If the mortar occupies $\frac{1}{10}$th of the volume of the wall,then find the number of bricks used in constructing the wall.

$A$ cylindrical bucket of height $32 \,cm$ and base radius $18 \,cm$ 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.

$A$ cone of radius $8 \, cm$ and height $12 \, cm$ is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of the two parts.