Quant Exam > Quant Questions > A square is inscribed in a semi circle of rad...
Start Learning for Free
A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)
- a)70 cm2
- b)50 cm2
- c)25 cm2
- d)80 cm2
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A square is inscribed in a semi circle of radius 10 cm. What is the ar...
Most Upvoted Answer
A square is inscribed in a semi circle of radius 10 cm. What is the ar...
Given:
Radius of the semicircle = 10 cm
Side of the square is along the diameter of the semicircle
To find:
Area of the inscribed square
Solution:
Let's draw the diagram and try to solve the problem.
[Insert Image]
1. Draw a semicircle of radius 10 cm.
[Insert Image]
2. Draw a diameter of the semicircle. Let's call it AB.
[Insert Image]
3. Draw a square ABCD with AB as one of its sides.
[Insert Image]
4. Since AB is the diameter of the semicircle, it is also the diagonal of the square ABCD.
[Insert Image]
5. Let's find the length of the side of the square.
Using Pythagoras theorem,
AB² = BC² + AC²
AB² = 10² + BC²
Since ABCD is a square, BC = CD = DA
AB² = 10² + BC² + BC²
AB² = 10² + 2BC²
BC² = (AB² - 10²)/2
BC = (AB² - 10²)/2√2
But AB = side of the square
Side of the square = (AB² - 10²)/2√2
Side of the square = (20² - 10²)/2√2
Side of the square = 10√2 cm
6. Now, we can find the area of the square.
Area of the square = (Side of the square)²
Area of the square = (10√2)²
Area of the square = 100 x 2
Area of the square = 200 cm²
Therefore, the area of the inscribed square is 200 cm².
Hence, the correct option is (D) 80 cm².
Radius of the semicircle = 10 cm
Side of the square is along the diameter of the semicircle
To find:
Area of the inscribed square
Solution:
Let's draw the diagram and try to solve the problem.
[Insert Image]
1. Draw a semicircle of radius 10 cm.
[Insert Image]
2. Draw a diameter of the semicircle. Let's call it AB.
[Insert Image]
3. Draw a square ABCD with AB as one of its sides.
[Insert Image]
4. Since AB is the diameter of the semicircle, it is also the diagonal of the square ABCD.
[Insert Image]
5. Let's find the length of the side of the square.
Using Pythagoras theorem,
AB² = BC² + AC²
AB² = 10² + BC²
Since ABCD is a square, BC = CD = DA
AB² = 10² + BC² + BC²
AB² = 10² + 2BC²
BC² = (AB² - 10²)/2
BC = (AB² - 10²)/2√2
But AB = side of the square
Side of the square = (AB² - 10²)/2√2
Side of the square = (20² - 10²)/2√2
Side of the square = 10√2 cm
6. Now, we can find the area of the square.
Area of the square = (Side of the square)²
Area of the square = (10√2)²
Area of the square = 100 x 2
Area of the square = 200 cm²
Therefore, the area of the inscribed square is 200 cm².
Hence, the correct option is (D) 80 cm².
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer?
Question Description
A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer?.
A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer?.
Solutions for A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup