$ABCD$ is a cyclic quadrilateral. $AB$ and $DC$ when produced meet at $P$. If $PA = 8 \ cm$,$PB = 6 \ cm$,and $PC = 4 \ cm$,then the length (in $cm$) of $PD$ is:

$A$ triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is $100 \, m$,then the altitude of the triangle is

$A$ cuboid of dimension $24 \text{ cm} \times 9 \text{ cm} \times 8 \text{ cm}$ is melted and smaller cubes of side $3 \text{ cm}$ are formed. Find how many such cubes can be formed?

The area of a parallelogram is $240 \, cm^{2}$ and its height is $12 \, cm$. The base of the parallelogram is ........ $cm$.

What is the radius of a circle,to the nearest $cm$,whose area is equal to the sum of the areas of the three circles of radii $22\, cm$,$19\, cm$,and $8\, cm$ respectively? (in $cm$)

$A$ rectangular tin sheet is $22 \ m$ long and $8 \ m$ broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. The volume of the cylinder (in $m^3$) is