The sides of a triangle having area $7776 \ cm^2$ are in the ratio $3:4:5$. The perimeter of the triangle is ........ $cm$.

The area of a sector of a circle of radius $5 \, cm$,formed by an arc of length $3.5 \, cm$,is ..... $cm^2$.

The area of a square is $196 \, cm^2$. Its side is half the radius of a circle. The circumference of the circle is equal to the breadth of a rectangle. If the perimeter of the rectangle is $712 \, cm$,what is the length of the rectangle? (in $cm$)

$A$ is the centre of a circle whose radius is $8$ and $B$ is the centre of a circle whose diameter is $8$. If these two circles touch externally,then the area of the circle with diameter $AB$ is $.........\pi$.

$A$ hollow spherical shell is made of a metal of density $4.9 \, g/cm^3$. If its internal and external radii are $10 \, cm$ and $12 \, cm$ respectively,find the weight of the shell. (Take $\pi = 3.1416$) (in $gm$)

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ $36.72$ per hectare is ₹ $495.72$,then find its base and height.