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

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is $8\, cm$ and the radius of the open end is $5\, cm$. When a few solid spherical metallic balls,each of radius $\frac{1}{2}\, cm$,are dropped into the vessel,$25\%$ of the water overflows. The number of balls is:

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

The radius of a cylinder is made twice as large. How should the height be changed so that its volume remains unchanged?

$A$ rectangular tin sheet is $12 \, cm$ long and $5 \, cm$ broad. It is rolled along its length to form a cylinder by making the opposite edges just touch each other. Then the volume of the cylinder is

The volume of a solid cylinder whose base diameter is $14\, mm$ and length is $25\, mm$ is $3850\, mm^3$. If the length of the cylinder is doubled but the diameter is halved,what will be the volume of the resulting cylinder? (in $mm^3$)