NCERT Solutions for Exercise 12.1 Class 10 Maths Chapter 12

NCERT Solutions for Exercise 12.1 Class 10 Maths Chapter 12 - Areas related to circles

Edited By Ramraj Saini | Updated on Nov 27, 2023 04:59 PM IST

NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1

NCERT Solutions for Exercise 12.1 Class 10 Maths Chapter 12 Areas related to circles are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. Class 10 Maths ex 12.1 includes the Introductory part of areas related to circles and the questions related to finding distance between the two circles out of some given conditions which are congruent or not, etc. The Numerical problems present in this introductory exercise is very important to cover in order to get better understanding of concepts. The Class 10 Maths chapter 12 exercise 12.1 lists a few practice problems on, circumference and area of Circle. The class 10th maths chapter 12 exercise 12.1 covers the topics like the concept of finding angles subtended by hour and minute hand in one or n revolutions . Also some properties and technical terms of circles enclosed with some special conditions

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NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1
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Benefits of NCERT Solutions for Class 10 Maths Chapter 12 Exercise 12.1
NCERT Solutions for Class 10 Subject Wise

NCERT Solutions for Exercise 12.1 Class 10 Maths Chapter 12 - Areas related to circles

10th class Maths exercise 12.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

Download Free PDF of NCERT Solutions for Class 10 Maths Chapter 12 Exercise 12.1

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Areas Related to Circles Class 10 Chapter 12 Exercise: 12.1

Q1 The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.

Answer:

Circumference of 1st circle is given :

$\\=\ 2\pi r_1\\\\=\ 2\pi \times 19\ =\ 38 \pi\ cm$

And the circumference of the 2nd circle is : $=\ 2\pi \times 9\ =\ 18 \pi\ cm$

Thus the circumference of the new circle is $=\ 18\pi\ +\ 38\pi\ =\ 56\pi\ cm$

or $2\pi r =\ 56\pi$

or $r\ =\ 28\ cm$

Hence the radius of the new circle is 28 cm.

Q2 The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having an area equal to the sum of the areas of the two circles.

Answer:

We know that the area of the circle is : $=\ \pi r^2$

Thus area of a 1st circle : $=\ \pi r^2_1$

or $=\ \pi \times 8^2\ =\ 64 \pi\ cm^2$

And the area of a 2nd circle is : $=\ \pi r^2_2$

or $=\ \pi \times 6^2\ =\ 36\pi\ cm^2$

According to the question area of the new circle is $=\ 64\pi\ +\ 36\pi\ =\ 100\pi\ cm^2$

or $\pi r^2\ =\ 100 \pi$

or $r\ =\ 10\ cm$

Hence the area of the new circle is 10 cm.

Q3 Fig. depicts an archery target marked with its five scoring regions from the center outwards as Gold, Red, Blue, Black, and White. The diameter of the region representing the Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Answer:

The radius of each scoring region can be found by adding 10.5 in respective colors.

The area of the golden region is : $=\ \pi r^2\ =\ \pi \times 10.5^2\ =\ 346.5\ cm^2$

Similarly area of the red region is = Area of a red score - Area of the golden region

$\\=\ \pi \times 21^2\ -\ \pi \times 10.5^2\\\\=\ 1039.5\ cm^2$

Then the area of the blue region is :

$\\=\ \pi \times (31.5)^2\ -\ \pi \times 21^2\\\\=\ 1732.5\ cm^2$

And the area of the black region is :

$\\=\ \pi \times 42^2\ -\ \pi \times (31.5)^2\\\\=\ 2425.5\ cm^2$

Area of the white region is :

$\\=\ \pi \times 52.5^2\ -\ \pi\times 42^2\\\\=\ 3118.5\ cm^2$

Q4 The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?

Answer:

Let the number of revolution of the wheel be n.

The circumference of the wheel is given by:-

$\\=\ 2\pi r\\\\=\ 2\pi \times 40\ =\ 80\pi\ cm$

Now, the speed of the car is given by:-

$\\=\ 66\ Km/hr\ \\\\=\ 66\times \frac{100000}{60}\ cm/min\ \\\\=\ 110000\ cm/min.$

Thus distance traveled in 10 minutes is: $=\ 1100000\ cm$

According to the question, we get;

$n\times 80\pi\ =\ 1100000$

or $n\ =\ 4375$

Hence the number of revolutions made by the wheel is 4372.

Q5 Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(A) 2 units
(B) $\pi$ units
(C) 4 units
(D) 7 units

Answer:

Let the radius of the circle be r.

Then according to question, we can write:-

Perimeter = Area

$\\2\pi r\ =\ \pi r^2\\\\r\ =\ 2\ units$

Hence option (A) is correct.

Benefits of NCERT Solutions for Class 10 Maths Chapter 12 Exercise 12.1

The very first benefits are already been mentioned in exercise 12.1 Class 10 Maths and the NCERT solutions for Class 10 Maths chapter 12 exercise 12.1 questions like equilateral triangle rolled around a circle and vertices are over it are discussed in this exercise.
Second most benefits is like in exercise 12.1 Class 10 Maths there are variety of concepts to understand in problem solving related to real life examples like wheel assembly of car and number of revolutions it is making under given conditions as discussed in Class 10 Maths chapter 12 exercise 12.1
For Class 10 final exams students may get MCQs, short numericals or long numericals questions from the type covered in the Class 10 Maths chapter 12 exercise 12.1

Also see-

NCERT Solutions for Class 10 Subject Wise

Frequently Asked Questions (FAQs)

1. Define Areas related to circles?

Ans The sectors between two radii and a neighbouring arc. A sector's area and a circle's segment: The sector of the circle is the portion of the circular region of the two radii and the associated arc is majorly called as area of circle.

2. What is the expression of area of segment of circle?

Ans: area of segment of circle = area of corresponding sector – area of corresponding triangle

3. How many total exercise are there in chapter 12 ?

Ans: There are total of 3 exercises there in chapter 12 namely exercise 12.1 exercise 12.2 and exercise 12.3 which have variety of questions to give a brief analysis of topic as well as subject.

4. How many parallel tangents does circle have?

Ans: A circle can have at most two parallel tangents.

5. What is the perimeter and area of unit circle ?

Ans: The radius of unit circle is 1 units

Hence Area = π

Perimeter = 2π

6. Which is the longest chord of circle and its length in terms of radius of circle?

Ans; The longest chord in circle is line segment of diameter and its length = 2*radius of circle

7. What is Areas of Combinations of Plane figures in chapter?

Ans: The majority of this part entails calculating the area of various shapes and patterns utilising a variety of planar figures and polygons. During the exam, the student should concentrate on mastering the formulas for determining the area of fundamental polygons.

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