# A stable owner has four horses He usually tie these horses

Q 37:- 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 buid 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

(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 cm ?             (1)

Solution:- (i) Length of the field = 20 m

Area of the square field = 20×20 = 400 m²

(ii)(a) Length of the rope = 7 m

The area of the field in which one horse can graze = 1/4 πr²

The area of the field in which four horse can graze = 4×1/4 πr²

=  πr² = π(7)²

= 49 π

OR

(ii) (a) The length of the rope of each horse is increased from 7 m to 10 m

New length of rope = 10 m

Area of field graze by one horse = 1/4 πr²

= 1/4 π(10)² = 25π

= 25×3.14 = 78.5 m²

(iii) The total area of the field grazes by four horse when length of the rope  7 m = 49 π

Total area of the field = 200 m²

The area of the field that is left ungrazed = 200 – 49 π

= 200 – 153.86

= 46.14 m²

Q 36:- Teaching Mathematics through activities is a powerful approach that enhances students understanding and angagement. Keeping this in mind, Ms. Mukta planed 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 passed 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 173250.                      [CBSE    2024]

Now, Mukta asked some questions 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)

Solution:- See full solution

Q 38:- 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 students 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.

rom the above answer the following question :

(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)

Solution:- See full solution