The radius of a cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder is

The material of a solid cone is converted into the shape of a solid cylinder of equal radius. If the height of the cylinder is $5\,cm$,then what is the height of the cone? (in $cm$)

The base of a right prism is a quadrilateral $ABCD$. Given that $AB = 9\, cm$,$BC = 14\, cm$,$CD = 13\, cm$,$DA = 12\, cm$ and $\angle DAB = 90^{\circ}$. If the volume of the prism is $2070\, cm^3$,then the area of the lateral surface is........$cm^2$.

$A$ cylindrical jar of diameter $24\, cm$ contains water to a height of $30\, cm$. $A$ spherical steel ball is dropped into the jar and the level of the water rises by $67.5\, mm$. The diameter of the ball is......$cm$.

$A$ cube of lead with edges measuring $6\, cm$ each is melted and recasted into $27$ equal cubes. The length of the edge of the new cube is.......$cm$

The volume of a cube is $729 \, cm^3$. The total surface area of the cube is ........ $cm^2$.