Math Problem Statement
Find the area
Find the area of the sector in the circle with a radius of 12 units and an angle of 0.5 radians.
Solution
To find the area of the sector shown in the image, we use the formula for the area of a sector of a circle:
Where:
- is the radius of the circle,
- is the angle in radians.
From the image:
- The radius ,
- The angle .
Now, let's compute the area .
Let me calculate that for you.The area of the sector is .
Would you like further details or have any other questions?
Here are 5 related questions you might find interesting:
- How do you calculate the area of a full circle?
- What is the circumference of a circle with radius 12 units?
- How would the area change if the angle were in degrees instead of radians?
- What is the formula for the length of an arc of a sector?
- How do you calculate the perimeter of a sector, including the arc length?
Tip: Always ensure that the angle in your formula is in radians when calculating areas or lengths related to circular sectors.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circle
Radians
Sector Area
Formulas
A = 1/2 * r^2 * θ
Theorems
Area of a sector of a circle
Suitable Grade Level
Grades 8-10