UPSC Exam > UPSC Questions > A circle is inscribed in an equilateral tria...
Start Learning for Free
A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?
- a)48
- b)72
- c)96
- d)54
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A circle is inscribed in an equilateral triangle of side 24 cm. What ...
Understanding the Problem
To find the area of the square inscribed in a circle that is inscribed in an equilateral triangle with a side length of 24 cm, we follow these steps.
Step 1: Calculate the Radius of the Inscribed Circle
- The radius (r) of the inscribed circle in an equilateral triangle can be calculated using the formula:
r = (side * √3) / 6
- For a triangle with a side of 24 cm:
r = (24 * √3) / 6 = 4√3 cm
Step 2: Determine the Diameter of the Circle
- The diameter (D) of the inscribed circle is:
D = 2 * r = 2 * 4√3 = 8√3 cm
Step 3: Find the Side Length of the Inscribed Square
- The side length (s) of the square inscribed in the circle is equal to the diameter divided by √2:
s = D / √2 = (8√3) / √2 = 8√(3/2) = 8√1.5 = 8 * 1.2247 ≈ 9.798 cm
Step 4: Calculate the Area of the Inscribed Square
- The area (A) of the square is given by:
A = s^2
- Therefore:
A = (8√(3/2))^2 = 64 * (3/2) = 96 cm²
Conclusion
The area of the square inscribed in the circle that is inscribed within the equilateral triangle is 96 cm². Thus, the correct answer is option 'C'.
To find the area of the square inscribed in a circle that is inscribed in an equilateral triangle with a side length of 24 cm, we follow these steps.
Step 1: Calculate the Radius of the Inscribed Circle
- The radius (r) of the inscribed circle in an equilateral triangle can be calculated using the formula:
r = (side * √3) / 6
- For a triangle with a side of 24 cm:
r = (24 * √3) / 6 = 4√3 cm
Step 2: Determine the Diameter of the Circle
- The diameter (D) of the inscribed circle is:
D = 2 * r = 2 * 4√3 = 8√3 cm
Step 3: Find the Side Length of the Inscribed Square
- The side length (s) of the square inscribed in the circle is equal to the diameter divided by √2:
s = D / √2 = (8√3) / √2 = 8√(3/2) = 8√1.5 = 8 * 1.2247 ≈ 9.798 cm
Step 4: Calculate the Area of the Inscribed Square
- The area (A) of the square is given by:
A = s^2
- Therefore:
A = (8√(3/2))^2 = 64 * (3/2) = 96 cm²
Conclusion
The area of the square inscribed in the circle that is inscribed within the equilateral triangle is 96 cm². Thus, the correct answer is option 'C'.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer?
Question Description
A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer?.
A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer?.
Solutions for A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of the square inscribed in the circle?a)48b)72c)96d)54Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC 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