In a right-angled triangle,find the hypotenuse if the base and perpendicular are respectively $36015 \ cm$ and $48020 \ cm$.

$A$ conical iron piece having diameter $28 \, cm$ and height $30 \, cm$ is totally immersed into the water of a cylindrical vessel,resulting in the rise of water level by $6.4 \, cm$. The diameter,in $cm$,of the vessel is

In a swimming pool measuring $90\, m$ by $40\, m$,$150$ men take a dip. If the average displacement of water by a man is $8\, m^3$,what will be the rise in water level? (in $cm$)

In the given figure,there is a large semicircle with diameter $AB = 56 \ cm$. Inside this,there are four smaller identical semicircles with diameters $AE, EF, FG,$ and $GB$ along the diameter $AB$. $A$ circle is inscribed such that it is tangent to the large semicircle and the two middle smaller semicircles. What is the area (in $cm^2$) of the shaded region?

The circumference of a circular field is $440 \, m$. $A$ circular path of $10 \, m$ width runs around the outside of the field. Find the cost of gravelling the path at the rate of $70 \, \text{paise}$ per square metre? (in $Rs.$)

The volume of a cube is $216 \, cm^3$. Part of this cube is then melted to form a cylinder of length $8 \, cm$. Find the volume of the cylinder (in $cm^3$)?