The figure below shows sketch of a base made around a large Gulmohar tree with cylindrical stem. The measure of its edges are given in the figure. 

The circumeference of the tree is $?$

In the picture below, the circumference of the front wheel is $2.2 \mathrm{m}$ and the distance from the centre of front wheel to pedal, $PO=70 \mathrm{cm}$. The distance from joint $B \mathrm{to} A$ on the handle bar is $5 \mathrm{cm}.$

Estimate the length of the rod $\mathrm{PA}.$

Below is the rough sketch of a roller with a handle to push over the soil and a stand to keep the roller steady when resting on the ground. Two rods are welded on the circular roller shield and their other ends are fixed at the centre of the handle. Two radial spokes each $50 \mathrm{cm}$ long, connect the roller shield with the centre of the roller. There is also a third rod $1.3 \mathrm{m}$ long, that connects the centre of the roller and the centre of the handle. 

The region shaded in the picture is to be covered by an iron sheet on both sides of the frame. Estimate the cost of an iron sheet if it costs $₹800 \mathrm{per} \mathrm{sq} \mathrm{m}$.

In a fun experiment, two objects being made to move along circular path of radius $15 \mathrm{cm}$ at a uniform speed of $5 \mathrm{m}/\mathrm{s}$. The objects where released simultaneously and their locations on the path were $\mathrm{A} \mathrm{and} \mathrm{B}$. The objects collided at location $\mathrm{O}$ in $4$ seconds. Find the distance of the point of collision from the centre of the circular path.

Below is the design of a football trophy designed by a football club for their tournaments. A cavity is made at the base of a solid circular cone to fit a sphere of radius $13 \mathrm{cm}$ on its top. The diameter of the base of cone is $24 \mathrm{cm}$ and its height is $20 \mathrm{cm}$. Find the height of the trophy.

A welder welded two circular rings with two iron rods as shown in the figure below. The radius of the rings are $10 \mathrm{cm}$ and $5 \mathrm{cm}$. If the distance between the centres of the rings is $15 \mathrm{cm}$, find the total length of both rods.

The hanging flower pot in the picture below has spherical container supported by $4$ chains. The distance from the topmost point to the centre of curvature of the spherical container is $60 \mathrm{cm}$. The radius of curvature of the container is $15 \mathrm{cm}$.

Find the total length of the chain required to hang the flower pot.

The shaded portion in the figure below is the portion of a paper that a child wants to use for making a kite. 

Find the area of the shaded portion.