In Text Questions Try These (Text Book Page No. 23,33,35 - Chapter 2 Measurements Term 2 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

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On April 24, 2024, 11:35 AM

Text Questions  : Chapter 2 Measurements  Term 2 Class 7th std Maths Guide Samacheer Kalvi Solutions
Exercise $2.1$
Try These (Text book Page No. 23)
Question $1 .$
A few real life examples of circular shapes are given below.

Can you give three more examples.
Solution:
1. One and Two rupee coins
2. Bangles
3. Mouth of Bottle
 

Question $2 .$
Find the diameter of your bicycle wheel?
Solution:
Diameter of my bicycle wheel is $700 \mathrm{~mm}$

Question $3 .$
If the diameter of the circle is $14 \mathrm{~cm}$, what will be it's radius?
Solution:
diameter $\mathrm{d}=14 \mathrm{~cm}$
radius $=\frac{d}{2}=\frac{14}{2}=7 \mathrm{~cm}$

Question $4 .$
If the radius of a bangle is 2 inches then find the diameter.
Solution:
Given radius of the bangle $=2$ inches
Diameter $=2 \times$ radius $=2 \times 2=4$ inches

Exercise $2.2$
Try These (Text book Page No. 33)
Question $1 .$
Draw circles of different radii on a graph paper. Find the area by counting the number of squares covered by the circle. Also find the area by using the formula.
(i) Find the area of the circle, if the radius is $4.2 \mathrm{~cm}$.
(ii) Find the area of the circle if the diameter is $28 \mathrm{~cm}$.
Solution:
(i) Radius of the circle $\mathrm{r}=4.2 \mathrm{~cm}$
Area of the circle $\mathrm{A}=\pi \mathrm{r}^{2}$ sq.units
$=\frac{22}{7} \times 4.2 \times 4.2 \mathrm{~cm}^{2}=5.44 \mathrm{~cm}^{2}$

(ii) Diameter of the circle $\mathrm{d}=28 \mathrm{~cm}$
radius $\mathrm{r}=\frac{d}{2}=\frac{28}{2}=14 \mathrm{~cm}$
Area of the circle $\mathrm{A}=\pi \mathrm{r}^{2}$ sq.units
$=\frac{22}{7} \times 14 \times 14 \mathrm{~cm}^{2}=616 \mathrm{~cm}^{2}$

Exercise $2.3$
Try These (Text book Page No. 35 )
Question $1 .$
If the outer radius and inner radius of the circles are respectively $9 \mathrm{~cm}$ and $6 \mathrm{~cm}$, find the width of the circular pathway.
Solution:
Radius of the outer circle $\mathrm{R}=9 \mathrm{~cm}$
Radius of the inner circle $\mathrm{r}=6 \mathrm{~cm}$
Width of the circular pathway = Radius of the outer circle
- Radius of the inner circle
$=(9-6) \mathrm{cm}=3 \mathrm{~cm}$
Width of the circular pathway $=3 \mathrm{~cm}$

Question $2 .$
If the area of the circular pathway is 352 sq.cm and the outer radius is $16 \mathrm{~cm}$, find the inner radius.
Solution:
Given outer radius $\mathrm{R}=16 \mathrm{~cm}$
Area of the circular pathway $=\pi R^{2}=\pi r^{2}$
Area of the circular pathway $=352$ sq. $\mathrm{cm}$
$\pi R^{2}-\pi r^{2}=352 \mathrm{~cm}^{2}$
$\pi\left(\mathrm{R}^{2}-\mathrm{r}^{2}\right)=352$
$16^{2}-\mathrm{r}^{2}=\frac{352 \times 7}{22}$
$16^{2}-r^{2}=16 \times 7$
$16^{2}-r^{2}=112$
$16^{2}-112=\mathrm{r}^{2}$
$r^{2}=256-112$
$r^{2}=144$
$\mathrm{r}=12 \mathrm{~cm}$
Inner radius $\mathrm{r}=12 \mathrm{~cm}$
 

Question $3 .$
If the area of the inner rectangular region is 15 sq.cm and the area covered by the outer rectangular region is 48 sq.cm, find the area of the rectangular pathway. Area of the outer rectangle Area of the inner rectangle Area of the rectangular pathway
Solution:
Area of the outer rectangle $=48$ sq.cm
Area of the inner rectangle $=15$ sq.cm
Area of the rectangular pathway = Area of the outer rectangle
- Area of the inner rectangle
$=48-15=33 \mathrm{~cm}^{2}$