In a circle centered at point O, the ratio of the area of sector AOB to the area of the circle is . What is the approximate measure, in radians, of the central angle corresponding to ? Round the answer to two decimal places
3.77
To find the measure of the central angle corresponding to the given ratio, we need to use the formula for the area of a sector of a circle. The formula is:
Area of a sector = (θ/2π) × πr²
Where θ is the measure of the central angle and r is the radius of the circle.
Given that the ratio of the area of sector AOB to the area of the circle is , we can set up the following equation:
θ/2π =
To find the value of θ, we need to solve for it in the equation. Rearranging the equation, we have:
θ = 2π ×
Now we can substitute the given value of the ratio into the equation and calculate the approximate measure of the central angle.
θ ≈ 2π ×
Next, we can plug in the given value for and calculate the approximate measure of θ. To round the answer to two decimal places, we will use the correct rounding rules.
For example, if the given ratio is = 0.25, we can substitute this value into the equation:
θ ≈ 2π × 0.25
θ ≈ 1.57 radians
Therefore, the approximate measure of the central angle corresponding to the given ratio is 1.57 radians, rounded to two decimal places.
To find the measure of the central angle corresponding to a ratio of areas, we can use the formula:
Central Angle = (Ratio of areas) * 2π radians
In this case, the ratio of the area of sector AOB to the area of the circle is given as . We need to find the central angle in radians.
Step 1: Substitute the given ratio into the formula.
Central Angle = (0.16) * 2π radians
Step 2: Calculate the approximate value of 2π.
2π is approximately equal to 6.28 radians (since π is approximately equal to 3.14).
Step 3: Substitute the value of 2π into the formula.
Central Angle = (0.16) * 6.28 radians
Step 4: Calculate the value of the central angle.
Central Angle ≈ 1.0048 radians (rounded to two decimal places)
Therefore, the approximate measure of the central angle corresponding to a ratio of areas is 1.00 radians.
a = 1/2 r^2 θ
Use that once you supply the missing data.