The ratio of the radius and slant height of a cone is $3:5$ and its curved surface area is $423.9 \, cm^2$. Find its volume. $(\pi = 3.14)$ (in $cm^3$)

In $\Delta ABC$,$\angle B = 90^{\circ}$,$AB = 6.3 \, cm$,and $BC = 8.4 \, cm$. If the triangle is revolved about the side $AB$,find the volume of the cone so obtained. Similarly,if the triangle $ABC$ is revolved about the side $BC$,find the volume of the cone so obtained.

The surface area of a cube whose edge is $a$ is: (in $a^{2}$)

The volume of a cuboid with length $25\, cm$ and breadth $15\, cm$ is equal to the volume of a cube with edge $15\, cm$. Find the height of the cuboid (in $cm$).

State whether the following statement is true or false:
The ratio of the surface areas of two spheres is $81: 49$. Then,the ratio of their volumes is $729: 343$.

$A$ sphere and a cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?