The largest cone is formed at the base of a cube of side measuring $7 \ cm$. Find the ratio of the volume of the cone to the volume of the cube.

$A$ square field with side $30\, m$ is surrounded by a path of uniform width. If the area of the path is $256\, m^2$,then its width is ........ $m$.

The length of a rectangle exceeds its breadth by $3 \, cm$. If the numerical values of the area and the perimeter of the rectangle are equal,then the breadth is ...... $cm$.

What is the radius of a circle,to the nearest $cm$,whose area is equal to the sum of the areas of the three circles of radii $22\, cm$,$19\, cm$,and $8\, cm$ respectively? (in $cm$)

On decreasing each side of an equilateral triangle by $2\, cm$,there is a decrease of $4\sqrt{3}\, cm^2$ in its area. The length of each side of the triangle is.........$cm$.

In a triangle $ABC$,$AB + BC = 12 \text{ cm}$,$BC + CA = 14 \text{ cm}$,and $CA + AB = 18 \text{ cm}$. Find the radius of the circle (in $\text{cm}$) which has the same perimeter as the triangle.