Exercise 2.1 - Chapter 2 Measurements Term 2 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $2.1$
Question $1 .$
Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

Solution:
(i) Given radius $\mathrm{r}=15 \mathrm{~cm}$
$\therefore$ diameter $\mathrm{d}=2 \times 15=30 \mathrm{~cm}$
Circumference $\mathrm{C}=\pi \mathrm{d}$ units
$=\frac{22}{7} \times 30=\frac{660}{7}=94.28 \mathrm{~cm}$
(ii) Given circumference $\mathrm{C}=1760 \mathrm{~cm}$
$2 \pi r=1760$
$2 \times \frac{22}{7} \times \mathrm{r}=1760$
$\mathrm{r}=\frac{1760 \times 7}{2 \times 22}=\frac{160 \times 7}{2 \times 2}=40 \times 7=280 \mathrm{~cm}$
diameter $=2 \times r$
$=2 \times 280=560 \mathrm{~cm}$
(iii) diameter $\mathrm{d}=24 \mathrm{~m}$
radius $\mathrm{r}=\frac{d}{2}=\frac{24}{2}=12 \mathrm{~m}$
Circumference $\mathrm{C}=2 \pi \mathrm{r}$ units
$=2 \times \frac{22}{7} \times 12=\frac{528}{7}=75.4 \mathrm{~m}$

Question 2 .
Diameters of different circles are given below. Find their circumference (Take $\pi=\frac{22}{7}$ )
(i) $\mathrm{d}=70 \mathrm{~cm}$
(ii) $\mathrm{d}=56 \mathrm{~m}$
(iii) $\mathrm{d}=28 \mathrm{~mm}$
Solution:
(i) Diameter $\mathrm{d}=70 \mathrm{~cm}$
Circumference $\mathrm{C}=\pi \mathrm{d}$ units $=\frac{22}{7} \times 70=22 \times 10=220 \mathrm{~cm}$
(ii) Diameter $\mathrm{d}=56 \mathrm{~m}$
Circumference $=\pi$ d units
$=\frac{22}{7} \times 56=22 \times 8=176 \mathrm{~m}$
(iii) Diameter $\mathrm{d}=28 \mathrm{~mm}$
Circumference $\mathrm{C}=\pi \mathrm{d}$ units $=\frac{22}{7} \times 28=22 \times 4=88 \mathrm{~mm}$
 

Question $3 .$
Find the circumference of the circles whose radii are given below.
(i) $49 \mathrm{~cm}$
(ii) $91 \mathrm{~mm}$
Solution:
Radius $\mathrm{r}=49 \mathrm{~cm}$
Circumference $\mathrm{C}=2 \pi \mathrm{r}$ units $=2 \times \frac{22}{7} \times 49=2 \times 22 \times 7$
$=44 \times 7=308 \mathrm{~cm}$
(ii) Radius $\mathrm{r}=91 \mathrm{~mm}$
Circumference $\mathrm{C}=2 \pi \mathrm{r}$ units
$=2 \times \frac{22}{7} \times 91=2 \times 22 \times 13=44 \times 13=572 \mathrm{~mm}$

Question $4 .$
The diameter of a circular well is $4.2 \mathrm{~m}$. What is its circumference?
Solution:
Given the diameter $\mathrm{d}=4.2 \mathrm{~m}$
Circumference $\mathrm{C}=\pi \mathrm{d}$ units $=\frac{22}{7} \times 4.2 \mathrm{~m}=22 \times 0.6=13.2 \mathrm{~m}$
 

Question $5 .$
The diameter of the bullock cart wheel is $1.4 \mathrm{~m}$. Find the distance covered by it in 150 rotations?
Solution:
Diameter of the bullock cart wheel $\mathrm{d}=1.4 \mathrm{~m}$
Distance covered in 1 rotation $=$ Its circumference
$=\pi \mathrm{d}$ units $=\frac{22}{7} \times 1.4 \mathrm{~m}=22 \times 0.2=4.4 \mathrm{~m}$
Distance covered in one rotation $=4.4 \mathrm{~m}$
Distance covered in 150 rotations $=4.4 \times 150=660.0$
Distance covered in 150 rotations $=660 \mathrm{~m}$

Question $6 .$
A ground is in the form of a circle whose diameter is $350 \mathrm{~m}$. An athlete makes 4 revolutions. Find the distance covered by the athlete.
Solution:
Diameter of the ground $\mathrm{d}=350 \mathrm{~m}$
Distance covered in 1 revolution = Circumference of the circle
$=\pi \mathrm{d}$ units $=\frac{22}{7} \times 350 \mathrm{~m}=22 \times 50=1100 \mathrm{~m}$
Distance covered in 1 rotation $=1100 \mathrm{~m}$
Distance covered in 4 revolutions $=1100 \times 4=4400 \mathrm{~m}$
 

Question $7 .$
A wire of length $1320 \mathrm{~cm}$ is made into circular frames of radius $7 \mathrm{~cm}$ each. How many frames can be made?
Solution:
Length of the wire $=1320 \mathrm{~cm}$
Radius of each circular frame $=7 \mathrm{~cm}$
Circumference of the frame $2 \pi \mathrm{r}$ units $=2 \times \frac{22}{7} \times 7 \mathrm{~cm}=2 \times 22=44 \mathrm{~cm}$
$\therefore$ Number of frames made $=\frac{\text { length of the wire }}{\text { circumference of one frame }}=\frac{1320}{44}=30$
30 frames can be made.
 

Question $8 .$
A Rose garden is in the form of circle of radius $63 \mathrm{~m}$. The gardener wants to fence it at the rate of $₹ 150$ per metre. Find the cost of fencing?
Solution:
Radius of the garden $\mathrm{r}=63 \mathrm{~m}$
Circumference of the garden $=2 \pi \mathrm{r}$ units $=2 \times \frac{22}{7} \times 63 \mathrm{~m}=2 \times 22 \times 9=396 \mathrm{~m}$
Cost of fencing 1 meter $=₹ 150$
Cost of fencing 396 meter $=₹ 150 \times 396=₹ 59,400$
$\therefore$ Cost of fencing the garden $=₹ 59,400$

Question $9 .$
Formula used to find the circumference of a circle is
(i) $2 \pi \mathrm{r}$ units
(ii) $\pi \mathrm{r}^{2}+2 \mathrm{r}$ units
(iii) $\pi \mathrm{r}^{2}$ sq. units
(iv) $\pi \mathrm{r}^{3} \mathrm{cu}$. units
Answer:
(i) $2 \pi \mathrm{r}$ units

Question $10 .$
In the formula, $\mathrm{C}=2 \pi \mathrm{r}, ~ ' \mathrm{r}$ ' refers to
(i) circumference
(ii) area
(iii) rotation
(iv) radius
Answer:
(iv) radius

Question $11 .$
If the circumference of a circle is $82 \pi$, then the value of ' $r$ ' is
(i) $41 \mathrm{~cm}$
(ii) $82 \mathrm{~cm}$
(iii) $21 \mathrm{~cm}$
(iv) $20 \mathrm{~cm}$
Answer:
(i) $41 \mathrm{~cm}$
 

Question $12 .$
Circumference of a circle is always
(i) three times of its diameter
(ii) more than three times of its diameter
(iii) less than three times of its diameter
(iv) three times of its radius
Answer:
(ii) more than three times of its diameter