The dome of a temple is in the shape of a cone with radius $3.5\, m$ and height $12\, m$. Find the cost of painting its outer surface at the rate of ₹ $30/m^2$.

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 $6 \pi r^{2}$.

$A$ cone of maximum size is carved out from a cube of edge $14 \, cm$. Find the surface area of the cone and the surface area of the remaining solid left after the cone is carved out.

The radii of a bucket in the shape of a frustum of a cone are $28 \, cm$ and $21 \, cm$. If its capacity is $28.490 \, \text{litres}$, find its height in $cm$.

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 $cm^2$)

The ratio of radii of two spheres is $2:3$. Then,the ratio of their volumes is $\ldots \ldots \ldots \ldots$.