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The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is a)(164 � 3) cm2 b)(163.62 � 2.6) cm2 c)(163.6 � 2.6) cm2 d)(163.62 � 3) cm2 Correct answer is option 'A'. Can you explain why the option 'A" is correct?
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The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm,...
Understanding Area Calculation
To find the area of a rectangle, we multiply the length by the breadth. Given the dimensions:
- Length = 16.2 cm
- Breadth = 10.1 cm
The area \( A \) is calculated as:
A = Length × Breadth = 16.2 cm × 10.1 cm
Calculating the Area
When performing the multiplication:
16.2 × 10.1 = 163.62 cm²
Significant Figures
Next, we need to consider significant figures. The number of significant figures in a measurement is determined by the least precise measurement.
- Length (16.2 cm) has 3 significant figures.
- Breadth (10.1 cm) also has 3 significant figures.
Thus, the area should be reported with 3 significant figures.
Final Area Representation
Since the area calculated is 163.62 cm², rounding it to 3 significant figures gives:
Area ≈ 164 cm²
Error Calculation
Now, let’s calculate the error. The relative error can be approximated by considering the errors in the original measurements:
- Error in Length = ±0.1 cm
- Error in Breadth = ±0.1 cm
Using the propagation of uncertainty for multiplication:
Relative error in area = (error in length / length) + (error in breadth / breadth)
This results in:
Relative error = (0.1/16.2) + (0.1/10.1) ≈ 0.00617 + 0.00990 ≈ 0.01607
Thus, the absolute error in the area = Area × relative error ≈ 163.62 × 0.01607 = 2.62 cm², which rounds to ±3 cm².
Conclusion
Therefore, the area of the rectangular sheet, including the error, is appropriately expressed as:
(164 ± 3) cm², making option A the correct choice.
To find the area of a rectangle, we multiply the length by the breadth. Given the dimensions:
- Length = 16.2 cm
- Breadth = 10.1 cm
The area \( A \) is calculated as:
A = Length × Breadth = 16.2 cm × 10.1 cm
Calculating the Area
When performing the multiplication:
16.2 × 10.1 = 163.62 cm²
Significant Figures
Next, we need to consider significant figures. The number of significant figures in a measurement is determined by the least precise measurement.
- Length (16.2 cm) has 3 significant figures.
- Breadth (10.1 cm) also has 3 significant figures.
Thus, the area should be reported with 3 significant figures.
Final Area Representation
Since the area calculated is 163.62 cm², rounding it to 3 significant figures gives:
Area ≈ 164 cm²
Error Calculation
Now, let’s calculate the error. The relative error can be approximated by considering the errors in the original measurements:
- Error in Length = ±0.1 cm
- Error in Breadth = ±0.1 cm
Using the propagation of uncertainty for multiplication:
Relative error in area = (error in length / length) + (error in breadth / breadth)
This results in:
Relative error = (0.1/16.2) + (0.1/10.1) ≈ 0.00617 + 0.00990 ≈ 0.01607
Thus, the absolute error in the area = Area × relative error ≈ 163.62 × 0.01607 = 2.62 cm², which rounds to ±3 cm².
Conclusion
Therefore, the area of the rectangular sheet, including the error, is appropriately expressed as:
(164 ± 3) cm², making option A the correct choice.
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The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is a)(164 � 3) cm2 b)(163.62 � 2.6) cm2 c)(163.6 � 2.6) cm2 d)(163.62 � 3) cm2 Correct answer is option 'A'. Can you explain why the option 'A" is correct?
Question Description
The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is a)(164 � 3) cm2 b)(163.62 � 2.6) cm2 c)(163.6 � 2.6) cm2 d)(163.62 � 3) cm2 Correct answer is option 'A'. Can you explain why the option 'A" is correct? for Interview Preparation 2024 is part of Interview Preparation preparation. The Question and answers have been prepared according to the Interview Preparation exam syllabus. Information about The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is a)(164 � 3) cm2 b)(163.62 � 2.6) cm2 c)(163.6 � 2.6) cm2 d)(163.62 � 3) cm2 Correct answer is option 'A'. Can you explain why the option 'A" is correct? covers all topics & solutions for Interview Preparation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is a)(164 � 3) cm2 b)(163.62 � 2.6) cm2 c)(163.6 � 2.6) cm2 d)(163.62 � 3) cm2 Correct answer is option 'A'. Can you explain why the option 'A" is correct?.
The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is a)(164 � 3) cm2 b)(163.62 � 2.6) cm2 c)(163.6 � 2.6) cm2 d)(163.62 � 3) cm2 Correct answer is option 'A'. Can you explain why the option 'A" is correct? for Interview Preparation 2024 is part of Interview Preparation preparation. The Question and answers have been prepared according to the Interview Preparation exam syllabus. Information about The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is a)(164 � 3) cm2 b)(163.62 � 2.6) cm2 c)(163.6 � 2.6) cm2 d)(163.62 � 3) cm2 Correct answer is option 'A'. Can you explain why the option 'A" is correct? covers all topics & solutions for Interview Preparation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is a)(164 � 3) cm2 b)(163.62 � 2.6) cm2 c)(163.6 � 2.6) cm2 d)(163.62 � 3) cm2 Correct answer is option 'A'. Can you explain why the option 'A" is correct?.
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