QQuestionMathematics
QuestionMathematics
"Find the area of the shaded sector of circle O.
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5π
20π
25π
50π"
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Answer
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Step 1:: Identify the information given in the problem.
We are given a circle with radius r = 5 units (since the diameter is 10 units). The sector is shaded with a central angle of θ = π/ 6 radians. We need to find the area of this shaded sector.
Step 2:: Recall the formula for the area of a sector.
A = rac{1}{2} r^{2} \theta
The area of a sector with radius r and central angle θ is given by the formula: where A is the area of the sector, r is the radius of the circle, and θ is the central angle in radians.
Step 3:: Plug in the values into the formula.
A = rac{1}{2} (5)^{2} (\frac{\pi}{6})
Now, we can use the given information to calculate the area of the shaded sector:
Step 4:: Simplify the expression.
A \approx 6.5 \text{ square units}
First, square the radius: Next, multiply the numbers: Finally, multiply the numbers to get the area:
Final Answer
The area of the shaded sector is approximately 6.5 square units.
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