If a cube with its edge $6 \ cm$ is melted and smaller cubes with edge $2 \ cm$ each are formed,then how many cubes are formed?

The radius of the base of a hollow cone is $8\, cm$ and its height is $15\, cm$. $A$ sphere of the largest possible radius is placed inside the cone. What is the ratio of the radius of the base of the cone to the radius of the sphere?

$A$ cone of height $7 \text{ cm}$ and base radius $3 \text{ cm}$ is carved from a rectangular block of wood $10 \text{ cm} \times 5 \text{ cm} \times 2 \text{ cm}$. The percentage of wood wasted is:

The cross section of a canal is in the shape of an isosceles trapezium which is $4 \ m$ wide at the bottom and $5 \ m$ wide at the top. If the depth of the canal is $2 \ m$ and it is $120 \ m$ long,what is the maximum capacity of this canal? (in $m^3$)

The numerical values of the volume and the area of the lateral surface of a right circular cone are equal. If the height of the cone is $h$ and the radius is $r,$ the value of $\frac{1}{h^{2}}+\frac{1}{r^{2}}$ is

$A$ cubic metre of silver weighing $900\, Kg$ is rolled into a $16\, m$ long square bar. Find out the weight of an exact cube cut off from it.