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The diagonals of rhombus ABCD intersect at O taking O as the centre and arc of radius 6 cm is drawn intersecting oa and OD at E and F respectively the area of the sector OEF is?
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The diagonals of rhombus ABCD intersect at O taking O as the centre an...
Understanding the Problem
To find the area of the sector OEF formed by the radius extending from point O to points E and F on a rhombus, we need to follow these steps:
Step 1: Identify Key Components
- Radius (r): Given as 6 cm.
- Sector OEF: This is the area we want to calculate.
Step 2: Determine the Angle
To find the area of the sector, we need the angle ∠EOF in radians. Since O is the intersection of the diagonals of rhombus ABCD, it divides the rhombus into four equal triangles. Each angle at O is 90°, as the diagonals of a rhombus bisect each other at right angles.
- Angle ∠EOF: 90° or π/2 radians.
Step 3: Calculate the Area of the Sector
The formula for the area of a sector is given by:
\[ \text{Area} = \frac{1}{2} r^2 \theta \]
Where:
- \( r \) = radius of the sector
- \( \theta \) = angle in radians
Applying the values:
- \( r = 6 \) cm
- \( \theta = \frac{\pi}{2} \)
Hence, the area becomes:
\[ \text{Area} = \frac{1}{2} \times (6)^2 \times \frac{\pi}{2} \]
\[ = \frac{1}{2} \times 36 \times \frac{\pi}{2} \]
\[ = 9\pi \, \text{cm}^2 \]
Final Result
The area of the sector OEF is \( 9\pi \, \text{cm}^2 \), which is approximately 28.27 cm² when calculated numerically.
To find the area of the sector OEF formed by the radius extending from point O to points E and F on a rhombus, we need to follow these steps:
Step 1: Identify Key Components
- Radius (r): Given as 6 cm.
- Sector OEF: This is the area we want to calculate.
Step 2: Determine the Angle
To find the area of the sector, we need the angle ∠EOF in radians. Since O is the intersection of the diagonals of rhombus ABCD, it divides the rhombus into four equal triangles. Each angle at O is 90°, as the diagonals of a rhombus bisect each other at right angles.
- Angle ∠EOF: 90° or π/2 radians.
Step 3: Calculate the Area of the Sector
The formula for the area of a sector is given by:
\[ \text{Area} = \frac{1}{2} r^2 \theta \]
Where:
- \( r \) = radius of the sector
- \( \theta \) = angle in radians
Applying the values:
- \( r = 6 \) cm
- \( \theta = \frac{\pi}{2} \)
Hence, the area becomes:
\[ \text{Area} = \frac{1}{2} \times (6)^2 \times \frac{\pi}{2} \]
\[ = \frac{1}{2} \times 36 \times \frac{\pi}{2} \]
\[ = 9\pi \, \text{cm}^2 \]
Final Result
The area of the sector OEF is \( 9\pi \, \text{cm}^2 \), which is approximately 28.27 cm² when calculated numerically.
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The diagonals of rhombus ABCD intersect at O taking O as the centre and arc of radius 6 cm is drawn intersecting oa and OD at E and F respectively the area of the sector OEF is?
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The diagonals of rhombus ABCD intersect at O taking O as the centre and arc of radius 6 cm is drawn intersecting oa and OD at E and F respectively the area of the sector OEF is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The diagonals of rhombus ABCD intersect at O taking O as the centre and arc of radius 6 cm is drawn intersecting oa and OD at E and F respectively the area of the sector OEF is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonals of rhombus ABCD intersect at O taking O as the centre and arc of radius 6 cm is drawn intersecting oa and OD at E and F respectively the area of the sector OEF is?.
The diagonals of rhombus ABCD intersect at O taking O as the centre and arc of radius 6 cm is drawn intersecting oa and OD at E and F respectively the area of the sector OEF is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The diagonals of rhombus ABCD intersect at O taking O as the centre and arc of radius 6 cm is drawn intersecting oa and OD at E and F respectively the area of the sector OEF is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonals of rhombus ABCD intersect at O taking O as the centre and arc of radius 6 cm is drawn intersecting oa and OD at E and F respectively the area of the sector OEF is?.
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