$A$ solid metallic hemisphere of radius $8 \, cm$ is melted and recast into a right circular cone of base radius $6 \, cm$. Determine the height of the cone (in $cm$).

The radius and height of a cone are both $3 \, cm$. Then,its volume is $\ldots \ldots \ldots \, cm^{3}$. (in $\pi$)

$A$ cistern,internally measuring $150 \,cm \times 120 \,cm \times 110 \,cm$,has $129600 \,cm^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water,each brick being $22.5 \,cm \times 7.5 \,cm \times 6.5 \,cm$?

Water flows at the rate of $10 \, m/min$ through a cylindrical pipe $5 \, mm$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40 \, cm$ and depth $24 \, cm$?

Write 'True' or 'False' and justify your answer:
$A$ spherical steel ball is melted to make eight new identical balls. Then,the radius of each new ball is $\frac{1}{8}$th the radius of the original ball.

The volume of a sphere is equal to $\ldots \ldots \ldots . .$