The base of a cone with radius $7\, cm$ and height $24\, cm$ is hemispherical. Find the cost of painting its surface at the rate of ₹ $2/cm^2$. (in ₹)

Write 'True' or 'False' and justify your answer:
$A$ spherical steel ball is melted to make eight new identical balls. Then,the radius of each new ball is $\frac{1}{8}$th the radius of the original ball.

The radii of three metallic spheres are $3 \, cm$,$4 \, cm$,and $5 \, cm$. These spheres are melted and recast into a single new sphere. Find the radius of the new sphere (in $cm$).

The ratio of the diameters of two cylinders is $3:4$ and the ratio of their heights is $4:5$. Then,the ratio of their volumes is ..... .

Write 'True' or 'False' and justify your answer:
The actual capacity of a vessel as shown in the figure is equal to the difference between the volume of the cylinder and the volume of the hemisphere.

If two solid hemispheres of same base radius $r$ are joined together along their bases, then the curved surface area of this new solid is (in $\pi r^{2}$)