The height of a cone is $30 \, cm$. $A$ small cone is cut off at the top by a plane parallel to the base. If its volume is $\frac{1}{27}$ of the volume of the given cone,at what height above the base is the section made? (in $cm$)

$A$ cylindrical can with a horizontal base and an internal radius of $3.5 \, cm$ contains sufficient water so that when a solid sphere is placed inside,the water just covers the sphere. The sphere fits exactly into the can. The depth of the water in the can before the sphere was added is:

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 the radius of a sphere is doubled,then its volume is increased by (in $\%$)

The height of a circular cylinder is increased $6$ times and the base area is decreased to $\frac{1}{9}$ of its value. The factor by which the lateral surface area of the cylinder increases is

The radius of the base of a conical tent is $5 \, m$. If the tent is $12 \, m$ high,then the area of the canvas required to make the tent is (in $\pi \, m^2$)