The radius and height of a right circular cone are in the ratio $5:12$. If its volume is $314 \frac{3}{7} \text{ m}^3$,find the radius of the cone (in $\text{m}$).

The portion of a ditch $48 \ m$ long, $16.5 \ m$ wide, and $4 \ m$ deep that can be filled with stones and earth available during the excavation of a tunnel, cylindrical in shape, of diameter $4 \ m$ and length $56 \ m$ is (Take $\pi = \frac{22}{7}$)

If three metallic spheres of radii $6\, cm$,$8\, cm$,and $10\, cm$ are melted to form a single sphere,the diameter of the new sphere will be (in $cm$)?

If each edge of a cube is increased by $50 \%$,the percentage increase in surface area is (in $\%$)

How many bricks are required to build a $15\, m$ long,$3\, m$ high,and $50\, cm$ thick wall,if each brick measures $25\, cm \times 12\, cm \times 6\, cm$?

$A$ cylindrical vessel of radius $4 \, cm$ contains water. $A$ solid sphere of radius $3 \, cm$ is lowered into the water until it is completely immersed. The water level in the vessel will rise by (in $cm$)