If a regular hexagon is inscribed in a circle of radius $r,$ then its perimeter is........$r$.

$A$ ladder is placed so as to reach a window $63 \ cm$ high. The ladder is then turned over to the opposite side of the street and is found to reach a point $56 \ cm$ high. If the ladder is $65 \ cm$ long,then the width of the street is........$cm$

$A$ tank $4 \, m$ long, $2.5 \, m$ wide, and $6 \, m$ deep is dug in a field $10 \, m$ long and $9 \, m$ wide. If the earth dugout is evenly spread over the field, the rise in level of the field will be (in $cm$):

$ABCD$ 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:

Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of $9856 \, m^{2}$. (in $m$)

$AB$ and $CD$ are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is $17 \, cm$. The lengths of $AB$ and $CD$ are $10 \, cm$ and $24 \, cm$ respectively. The radius (in $cm$) of the circle is