The base of a cone with radius $14 \, cm$ and height $32 \, cm$ is hemispherical. Find its volume in $cm^3$.

The radii of two $10 \, cm$ high metallic cylinders are $3.5 \, cm$ and $7 \, cm$. These cylinders are melted and recast to produce a cylinder with height $50 \, cm$. Find the radius of this new cylinder (in $cm$).

Two identical cubes each of volume $64 \, cm^{3}$ are joined together end to end. What is the surface area of the resulting cuboid? (in $cm^{2}$)

The formula to find the total surface area of a $5$-rupee coin is $A = \ldots$

Two cones with the same base radius $8\, cm$ and height $15\, cm$ are joined together along their bases. Find the surface area of the shape so formed. (in $cm^2$)

$A$ bucket is in the form of a frustum of a cone and holds $28.490 \, \text{litres}$ of water. The radii of the top and bottom are $28 \, \text{cm}$ and $21 \, \text{cm}$, respectively. Find the height of the bucket. (in $\text{cm}$)