Six wooden cubes of length $3 \, cm$ are arranged in a row touching each other face to face. Find the total surface area of the solid formed in this manner. (in $cm^2$)

The radii of two $10 \, cm$ high metallic cylinders are $3.5 \, cm$ and $7 \, cm$. These cylinders are melted and recast to produce a cylinder with height $50 \, cm$. Find the radius of this new cylinder (in $cm$).

The ratio of diameters of two cones is $2:3$ and the ratio of their heights is $9:4$. Then,the ratio of their volumes is:

$A$ cone of maximum size is carved out from a cube of edge $14 \, cm$. Find the surface area of the cone and the surface area of the remaining solid left after the cone is carved out.

The volume of a cylinder is $20 \pi \, cm^3$ and its height is $5 \, cm$. Then,the diameter of the cylinder is $\ldots \ldots \ldots \ldots \, cm$.

Water flows through a cylindrical pipe,whose inner radius is $1 \,cm$,at the rate of $80 \,cm/sec$ into an empty cylindrical tank,the radius of whose base is $40 \,cm$. What is the rise of water level in the tank in half an hour? (in $cm$)