Exercise 4.2 - Chapter 4 Geometry Term 3 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex 4.2
Question $1 .$
Draw circles for the following measurements of radius (r)/ diameters(d).
(i) $\mathrm{r}=4 \mathrm{~cm}$
(ii) $\mathrm{d}=12 \mathrm{~cm}$
(iii) $\mathrm{r}=3.5 \mathrm{~cm}$
(iv) $\mathrm{r}=6.5 \mathrm{~cm}$.
(v) $\mathrm{d}=6 \mathrm{~cm}$
Solution:
(i) $\mathrm{r}=4 \mathrm{~cm}$

Step 1 : Market a point ' $\mathrm{O}$ ' on the paper.
Step 2 : Extended the compass distance equal to radius $4 \mathrm{~cm}$.
Step 3 : At center 'O', helded the compass firmly and placed the pointed end of the compass.
Step 4 : Slowly rotated the compass around to get the circle.
(ii) $\mathrm{d}=12 \mathrm{~cm}$
given $\mathrm{d}=12 \mathrm{~cm}$

$\therefore$ radius $\mathrm{r}=\frac{d}{2}=\frac{12}{2}=6 \mathrm{~cm}$

Step 1: Marked a point ' $\mathrm{O}$ ' on the paper.
Step 2: Extended the compass distance equal to radius $6 \mathrm{~cm}$.
Step 3: At center ' $\mathrm{O}$ ', held the compass furmly and placed the pointed end of the compass. Step 4: Slowly rotated the compass around to get the circle.
(iii) $\mathrm{r}=3.5 \mathrm{~cm}$

Step 1: Market a point 'O' on the paper.
Step 2: Extended the compass distance equal to radius $3.5 \mathrm{~cm}$.
Step 3: At center ' $\mathrm{O}$ ', held the compass furmly and placed the pointed end of the compass.
Step 4: Slowly rotated the compass around to get the circle.
(iv) $\mathrm{r}=6.5 \mathrm{~cm}$

Step 1: Market a point ' $\mathrm{O}$ ' on the paper.
Step 2: Extended the compass distance equal to radius $6.5 \mathrm{~cm}$.
Step 3: At center ' $\mathrm{O}$ ', held the compass firmly and placed the pointed end of the compass. Step 4: Slowly rotated the compass around to get the circle.
(v) $\mathrm{d}=6 \mathrm{~cm}$
$\therefore$ radius $\mathrm{r}=\frac{d}{2}=\frac{6}{2}=3 \mathrm{~cm}$

Step 1: Market a point ' $\mathrm{O}$ ' on the paper.
Step 2: Extended the compass distance equal to radius $3 \mathrm{~cm}$.
Step 3: At center ' $\mathrm{O}$ ', held the compass firmly and placed the pointed end of the compass. Step 4: Slowly rotated the compass around to get the circle.

Question $2 .$
Draw concentric circles for the following measurements of radii / diameters. Find out the width of each circular ring.
(i) $r=3 \mathrm{~cm}$ and $r=5 \mathrm{~cm}$.
(ii) $\mathrm{r}=3.5 \mathrm{~cm}$ and $\mathrm{r}=6.5 \mathrm{~cm}$.
(iii) $\mathrm{d}=6.4 \mathrm{~cm}$ and $\mathrm{d}=11.6 \mathrm{~cm}$.
(iv) $r=5 \mathrm{~cm}$ and $r=7.5 \mathrm{~cm}$.
(vi) $\mathrm{r}=7.1 \mathrm{~cm}$ and $\mathrm{d}=12 \mathrm{~cm}$.
Solution:
(i) $r=3 \mathrm{~cm}$ and $r=5 \mathrm{~cm}$.

Width of the circular ring $=\mathrm{OB}-\mathrm{OA}=5-3=2 \mathrm{~cm}$
Step 1: Drawn a rough diagram and market the given measurements
Step2: Taken any point $\mathrm{O}$ and marked it as center.
Step 3: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OA}=3 \mathrm{~cm}$.
Step 4: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OB}=5 \mathrm{~cm}$. Thus concentric circles $C_{1}$ and $C_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}=5-3=2 \mathrm{~cm}$

(ii) $\mathrm{r}=3.5 \mathrm{~cm}$ and $\mathrm{r}=6.5 \mathrm{~cm}$

Step 1: Drawn a rough diagram and market the given measurements
Step 2: Taken any point $\mathrm{O}$ and marked it as the center.
Step 3: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OA}=3.5 \mathrm{~cm}$.
Step 4: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OB}=6.5 \mathrm{~cm}$. Thus the concentric circles $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}=6.5-3.5=3 \mathrm{~cm}$
(iii) $\mathrm{d}=6.4 \mathrm{~cm}$ and $\mathrm{d}=11.6 \mathrm{~cm}$
$\mathrm{r}=\frac{d}{2}$

$\mathrm{r}=\frac{6.4}{2}=3.2 \mathrm{~cm} ; \mathrm{r}=\frac{11.6}{2}=5.8 \mathrm{~cm}$

Step 1: Drawn a rough diagram and market the given measurements
Step 2: Taken any point $\mathrm{O}$ and marked it as the center.
Step 3: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OA}=3.2 \mathrm{~cm}$.
Step 4: With $\mathrm{O}$ as center and drawn a circle of radius $\mathrm{OB}=5.8 \mathrm{~cm}$. Thus the concentric circles $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}=5.8-3.2=2.6 \mathrm{~cm}$

(iv) $\mathrm{r}=5 \mathrm{~cm}$ and $\mathrm{r}=7.5 \mathrm{~cm}$
Step 1 : Drawn a rough diagram and market the given measurements
Step 2 : Taken any point $\mathrm{O}$ and marked it as the center.
Step 3: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OA}=5 \mathrm{~cm}$.
Step 4 : With $O$ as center drawn a circle of radius $O B=7.5 \mathrm{~cm}$. Thus the concentric circles $C_{1}$ and $C_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}=7.5-5=2.5 \mathrm{~cm}$
(v) $\mathrm{d}=6.2 \mathrm{~cm}$ and $\mathrm{r}=6.2 \mathrm{~cm}$.
$\mathrm{r}=\frac{d}{2}$

Step 1: Drawn a rough diagram and market the given measurements
Step 2 : Taken any point $\mathrm{O}$ and marked it as the center.
Step 3: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OA}=5 \mathrm{~cm}$.
Step 4: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OB}=7.5 \mathrm{~cm}$. Thus the concentric circles $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}=7.5-5=2.5 \mathrm{~cm}$
(v) $\mathrm{d}=6.2 \mathrm{~cm}$ and $\mathrm{r}=6.2 \mathrm{~cm}$.
$\mathrm{r}=\frac{d}{2}$

$\therefore \mathrm{r}=\frac{6.2}{2}=3.1 \mathrm{~cm}$ and $\mathrm{r}=6.2 \mathrm{~cm}$
Step 1: Drawn a rough diagram and market the given measurements Step 2: Taken any point $\mathrm{O}$ and marked it as the center.
Step 3: With $\mathrm{O}$ as center, drawn a circle of radius $\mathrm{OA}=3.1 \mathrm{~cm}$.
Step 4: With $\mathrm{O}$ as center, drawn a circle of radius $\mathrm{OB}=6.2 \mathrm{~cm}$.
Thus the concentric circles $C_{1}$ and $C_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}=6.2-3.1=3.1 \mathrm{~cm}$
(vi) $\mathrm{r}=7.1 \mathrm{~cm}$ and $\mathrm{d}=12 \mathrm{~cm}$.
$\mathrm{r}=\frac{d}{2}$

Step 1: Drawn a rough diagram and marked the given measurements
Step 2 : Taken any point $\mathrm{O}$ and marked it as center.
Step 3 : With $\mathrm{O}$ as center, drawn a circle of radius $\mathrm{OA}=6 \mathrm{~cm}$.
Step 4 : with $\mathrm{O}$ as center, drawn a circle of radius $\mathrm{OB}=7.1 \mathrm{~cm}$. Thus concentric circles $C_{1}$ and $C_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}=7.1-6=1.1 \mathrm{~cm}$