Embibe Experts Solutions for Chapter: Circles, Exercise 1: Exercise

A student created a logo for an upcoming sports event in the school. Below is the cutout of the model the student created. The radius of the circles are $3 \mathrm{cm}$ and $5 \mathrm{cm}$. The length from one end to the smaller circle is $4 \mathrm{cm}$ and from the other end to the larger circle is $12 \mathrm{cm}$.

The length of the logo is _____ $\mathrm{cm}$.

Two friends, as part of fun trip starts from a common point in two directions. Person $A$ went along $30° \mathrm{SE}$ with respect to the East and person $B$ went along $30° \mathrm{NE}$ with respect to the East.

Person $A$ travelled along a straight path till the periphery of a circular path, turned left, continued along the straight path to reach the centre of circular path, and paused. Person $B$ also reached the periphery of the circular path and asked person to join him.

Determine the angle person $A$ should turn at $C$, from his current direction to reach person $B$.

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 $₹800 \mathrm{per} \mathrm{sq} \mathrm{m}$.

The figure below is a sketch of a circular auditorium surrounded by circular park. The centre of auditorium and the park is the same. The diameters of the auditorium and the circular path are $40 \mathrm{m}$ and $120 \mathrm{m}$ respectively. A person going for a walk from location $\mathrm{A}$ to $\mathrm{B}$.

Find the minimum distance the person has to walk.

The picture below shows the path of two flower rockets fired from fixed point in a circus camp, brushed past a large circular ring of radius $40 \mathrm{m}$. Both rockets went past the ring in one second after they were fired simultaneously, at an average speed of $30 \mathrm{m}/\mathrm{s}$. 

Estimate the height of the centre of ring from the point where the rockets were fired.

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.