How do you calculate the area and arc length of region ABCD using given values?

MHB
Thread starter jevanuD
Start date Mar 30, 2018
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Arc Arc length Length

In summary, a radian is a unit of measurement for angles that is defined as the angle subtended by an arc of a circle with the same length as its radius. To convert degrees to radians, you can use a formula or a conversion chart. The arc length of a circle can be found by multiplying the central angle (in radians) by the radius, or by using the formula arc length = circumference * (central angle / 360) if the radius is unknown. Finding the arc length has practical applications in various real-life scenarios such as calculating distance and circumference.

Mar 30, 2018

jevanuD

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Mar 30, 2018

skeeter

area of region ABCD ...

$A = \dfrac{\theta}{2}\left(R^2-r^2\right)$

you have $R = 3k$, $r=2k$, and $\theta = \dfrac{3}{4}$

... proceed to solve for $k$

also, arc length difference is $\Delta s = \theta(R - r)$

Related to How do you calculate the area and arc length of region ABCD using given values?

1. What is a radian?

A radian is a unit of measurement commonly used in mathematics and physics to measure angles. It is defined as the angle subtended by an arc of a circle that has the same length as the circle's radius.

2. How do you convert degrees to radians?

To convert degrees to radians, you can use the formula radians = (degrees * π) / 180. Alternatively, you can use a calculator or a conversion chart to find the equivalent value in radians.

3. How do you find the arc length of a circle?

The arc length of a circle can be found by multiplying the central angle (in radians) by the radius of the circle. The formula for arc length is arc length = radius * central angle.

4. Can you find the arc length without knowing the radius?

Yes, you can find the arc length without knowing the radius by using the formula arc length = circumference * (central angle / 360). The circumference can be found by multiplying the diameter of the circle by π.

5. How is finding the arc length useful in real life?

Finding the arc length can be useful in various real-life applications such as calculating the distance traveled by a rotating object, determining the length of a curved road or track, and measuring the circumference of a circular object like a wheel or clock.