Each of the radius of a cylinder and a sphere is $9 \, cm$. If the volumes of these solids are equal,find the height of a cylinder (in $cm$).

The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base,using cardboard. Each penholder was to be of radius $3 \,cm$ and height $10.5 \,cm$. The Vidyalaya was to supply the competitors with cardboard. If there were $35$ competitors,how much cardboard was required to be bought for the competition (in $,cm^2$)? $\left[\text{Assume } \pi = \frac{22}{7}\right]$

The length of a metal hollow cylinder is $70\, cm$. If the radius of the hollow inside it is $10\, cm$ and the metal thickness is $1\, cm$,find the difference between the areas of the outer and inner curved surfaces.

The surface area of a sphere is $5544 \, cm^2$. Find its volume in $cm^3$.

The inner diameter of a cylindrical wooden pipe is $24 \, cm$ and its outer diameter is $28 \, cm$. The length of the pipe is $35 \, cm$. Find the mass of the pipe,if $1 \, cm^3$ of wood has a mass of $0.6 \, g$. (in $, kg$)

The edge of a cube is $6 \, cm$. Find the total surface area of the cube and the volume of the cube.