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8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:
i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.
ii) Find the number of vacant seats if maximum number of rows are occupied.
iii)To accommodate 1296 students how many rows will be occupied?
i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.
ii) Find the number of vacant seats if maximum number of rows are occupied.
iii)To accommodate 1296 students how many rows will be occupied?
Most Upvoted Answer
8. The planetarium is designed for 2000 seating capacity. Students are...
i) Maximum Number of Rows Occupied
To find the maximum number of rows occupied in the planetarium, we need to determine the largest perfect square that is less than or equal to the seating capacity of 2000.
- The largest integer \( n \) such that \( n^2 \leq 2000 \) is \( n = 44 \) (since \( 44^2 = 1936 \)).
- Therefore, the maximum number of rows occupied is 44.
ii) Number of Vacant Seats
To calculate the number of vacant seats when the maximum number of rows are occupied:
- Total seats in the planetarium = 2000
- Seats occupied when 44 rows are filled = \( 44 \times 44 = 1936 \)
- Vacant seats = Total seats - Occupied seats = \( 2000 - 1936 = 64 \)
Thus, there are 64 vacant seats.
iii) Rows Occupied for 1296 Students
To accommodate 1296 students, we will again look for the largest perfect square less than or equal to 1296:
- The largest integer \( m \) such that \( m^2 \leq 1296 \) is \( m = 36 \) (since \( 36^2 = 1296 \)).
- Thus, to accommodate 1296 students, 36 rows will be occupied.
In conclusion, the perfect square arrangement ensures that both rows and columns have equal seating, optimizing space usage in the planetarium effectively.
To find the maximum number of rows occupied in the planetarium, we need to determine the largest perfect square that is less than or equal to the seating capacity of 2000.
- The largest integer \( n \) such that \( n^2 \leq 2000 \) is \( n = 44 \) (since \( 44^2 = 1936 \)).
- Therefore, the maximum number of rows occupied is 44.
ii) Number of Vacant Seats
To calculate the number of vacant seats when the maximum number of rows are occupied:
- Total seats in the planetarium = 2000
- Seats occupied when 44 rows are filled = \( 44 \times 44 = 1936 \)
- Vacant seats = Total seats - Occupied seats = \( 2000 - 1936 = 64 \)
Thus, there are 64 vacant seats.
iii) Rows Occupied for 1296 Students
To accommodate 1296 students, we will again look for the largest perfect square less than or equal to 1296:
- The largest integer \( m \) such that \( m^2 \leq 1296 \) is \( m = 36 \) (since \( 36^2 = 1296 \)).
- Thus, to accommodate 1296 students, 36 rows will be occupied.
In conclusion, the perfect square arrangement ensures that both rows and columns have equal seating, optimizing space usage in the planetarium effectively.
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8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied?
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8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied?.
8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied?.
Solutions for 8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied? in English & in Hindi are available as part of our courses for UPSC.
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8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied?, a detailed solution for 8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied? has been provided alongside types of 8. The planetarium is designed for 2000 seating capacity. Students are required to be seated in such a way that the number of students in each row is equal to the number of students in each column. Based on the above information answer the following questions:i) Find the maximum number of rows occupied if planetarium is not filled to its capacity.ii) Find the number of vacant seats if maximum number of rows are occupied.iii)To accommodate 1296 students how many rows will be occupied? theory, EduRev gives you an
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