Case study 2:-
A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze. [CBSE 2024]
Based on the above, answer the following question :
(i) Find the area of the square shaped grass field . 1
(ii) (a) Find the area of the total field in which these horses can graze . 2
OR
(ii) (b) If the length of the rope of each horse is increased from 7 m to 10 m, find the area grazed by one horse. (Use π = 3.14) 2
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is 7 m ? 1
Solution:-
(i) Length of a square shaped grass field = 20 m
Area of a square shaped grass field = l × b
= 20 × 20 = 400 m²
(ii) (a) The length of rope to pegs at each corner of a square shaped grass field = 7 m
The area of the total field in which these horses can graze
= 4× πr²/4
= πr² = π (7)²
= 49 π = 49× 22/7
= 154 m²
The area of field graze by horses = 154 m²
OR
(ii) (b) The length of rope increase 7m to 20 m
Now the length of rope = 20 m
The area grazed by one horse = πr²/4
= 1/4 × 3.14 × 20× 20
= 314 m²
(iii) Total area of field = 400 m²
The area of the total field in which these horses can graze = 154 m²
Remaining area of field which is ungrazed
= 400 – 154
= 246 m²
Case study 1:
Teaching Mathematics through activities is a powerful approach that enhances students’ understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 1,73,250. [CBSE 2024]
Now, Mukta asked some question as given below to the students :
(i) What is the least prime number used by students ? 1
(ii) (a) How many students are in the class ? 2
OR
(ii) (b) What is the highest prime number used by student ? 2
(iii) Which prime number has been used maximum times ? 1
Solution: – See the full solution
Case study 3:-
Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job- specific skills, enhancing employability thus making the student self reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.
From the above answer the following questions: [CBSE 2024]
(i) What is the lower limit of the model class of the above data ? 1
(ii) (a) Find the median class of the above data. 2
OR
(b) Find the number of participants of age less than 50 years who undergo vocational training. 2
(iii) Give the empirical reletionship between mean, median and mode. 1
Solution: See the solution
