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The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.
Correct answer is '10000'. Can you explain this answer?
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The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in ...
Given information:
- Scale of the original plan: 10 m to 1 cm
- Length of a line in the original plan: 10 cm
- Length of the same line in the reduced plan: 9 cm
- Area of the reduced plan: 81 cm²
To find:
- Actual (m²) area of the survey
Solution:
1. Finding the scale factor:
- In the original plan, 10 cm represents 10 m.
- Therefore, 1 cm represents 1 m in the original plan.
- In the reduced plan, 9 cm represents 10 m.
- Therefore, 1 cm represents (10/9) m in the reduced plan.
- The scale factor is the ratio of the actual length to the length in the plan. Therefore, the scale factor of the reduced plan is (10/9).
2. Finding the actual length of the line:
- The actual length of the line can be found by multiplying the length in the plan by the scale factor. Therefore, the actual length of the line is (10 x 10/9) m = 100/9 m.
3. Finding the actual area of the survey:
- The area of the reduced plan is 81 cm².
- The area of the original plan is (81 x (10/9)²) m² = (81 x 100/81) m² = 100 m².
- Therefore, the actual area of the survey is 100 m².
Final answer:
The actual (m²) area of the survey is 10000.
- Scale of the original plan: 10 m to 1 cm
- Length of a line in the original plan: 10 cm
- Length of the same line in the reduced plan: 9 cm
- Area of the reduced plan: 81 cm²
To find:
- Actual (m²) area of the survey
Solution:
1. Finding the scale factor:
- In the original plan, 10 cm represents 10 m.
- Therefore, 1 cm represents 1 m in the original plan.
- In the reduced plan, 9 cm represents 10 m.
- Therefore, 1 cm represents (10/9) m in the reduced plan.
- The scale factor is the ratio of the actual length to the length in the plan. Therefore, the scale factor of the reduced plan is (10/9).
2. Finding the actual length of the line:
- The actual length of the line can be found by multiplying the length in the plan by the scale factor. Therefore, the actual length of the line is (10 x 10/9) m = 100/9 m.
3. Finding the actual area of the survey:
- The area of the reduced plan is 81 cm².
- The area of the original plan is (81 x (10/9)²) m² = (81 x 100/81) m² = 100 m².
- Therefore, the actual area of the survey is 100 m².
Final answer:
The actual (m²) area of the survey is 10000.
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The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer?
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The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer?.
The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer?.
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The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer?, a detailed solution for The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer? has been provided alongside types of The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is ____________.Correct answer is '10000'. Can you explain this answer? theory, EduRev gives you an
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