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Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements.
What is the circumference of a Semicircle?
I. The radius of the semicircle is equal to half the side of a square.
II. The area of the square is 196 sq.cm.
  • a)
    If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
  • b)
    if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
  • c)
    if the data in Statement I alone or in Statement II alone are sufficient to answer the question.
  • d)
    if the data in both the Statements I and II are not sufficient to answer the question.
  • e)
    if the data in both the Statements I and II together are necessary to answer the question.
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
Each of the questions below consists of a question and two statements...
Using statement I,
Radius = half of the side of the square
But the length of the side of a square is not known Using statement II:
Area of a square = 196
Side of a square = 14 cm
Combining both statements, radius of the circle can be calculated
Hence, option 5
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Most Upvoted Answer
Each of the questions below consists of a question and two statements...
Understanding the Problem
To find the circumference of a semicircle, we need to know its radius. The formula for the circumference of a semicircle is given by:
Circumference = πr + 2r
Where "r" is the radius of the semicircle.
Analyzing Statement I
- Statement I: The radius of the semicircle is equal to half the side of a square.
- This statement provides a relationship between the radius and the side of a square but does not give a numerical value for either. Thus, we cannot determine the actual radius from this statement alone.
Analyzing Statement II
- Statement II: The area of the square is 196 sq.cm.
- From this statement, we can calculate the side length of the square using the formula for area (Area = side²). Therefore, the side of the square is √196 = 14 cm.
- Since the radius of the semicircle is half the side of the square, the radius would be 14 cm / 2 = 7 cm.
Combining Both Statements
- Both statements together clarify the relationship between the square and the semicircle:
- From Statement II, we get the side of the square, and from Statement I, we find the radius of the semicircle.
- Thus, we can now substitute the radius back into the semicircle circumference formula.
Conclusion
- Neither statement alone is sufficient to answer the question. However, when combined, they provide all the necessary information to calculate the circumference of the semicircle. Therefore, the correct answer is option 'E': both statements together are necessary to answer the question.
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Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements.What is the circumference of a Semicircle?I. The radius of the semicircle is equal to half the side of a square.II. The area of the square is 196 sq.cm.a) If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.c) if the data in Statement I alone or in Statement II alone are sufficient to answer the question.d) if the data in both the Statements I and II are not sufficient to answer the question.e) if the data in both the Statements I and II together are necessary to answer the question.Correct answer is option 'E'. Can you explain this answer?
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