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 $cm$)

$A$ semicircular sheet of metal of diameter $28 \, cm$ is bent into an open conical cup. The capacity of the cup (taking $\pi = \frac{22}{7}$) is (in $cm^3$):

If a right circular cone of height $24\, cm$ has a volume of $1232\, cm^{3},$ then the area (in $cm^{2}$) of its curved surface is:

The perimeter of one face of a cube is $20 \, cm$. Its volume must be (in $cm^3$):

The height of a right circular cone and the radius of its circular base are $9 \, cm$ and $3 \, cm$ respectively. The cone is cut by a plane parallel to its base so as to divide it into two parts. The volume of the frustum (i.e.,the lower part) of the cone is $44 \, cm^3$. The radius of the upper circular surface of the frustum $\left(\text{taking } \pi = \frac{22}{7}\right)$ is

The radius of the base of a solid cone is $9\, cm$ and its height is $21\, cm$. It is cut into $3$ parts by two cuts which are parallel to its base. The cuts are at heights of $7\, cm$ and $14\, cm$ from the base respectively. What is the ratio of the curved surface areas of the top,middle,and bottom parts respectively?