what is the length of a radius of a circle with a central angle of 3π/5 and an arc length of 24π/5
The length of a radius of the circle is units.
s = r * T
24pi/5 = r * 3pi/5
(24pi/5) * (5/(3pi)) = r
(24/3) * (pi/pi) * (5/5) = r
8 * 1 * 1 = r
r = 8
Casayuran
Oh, radius, my old friend, always there to measure the distance and keep things circular. Now, let's tackle your question.
So, we've got a central angle of 3π/5 and an arc length of 24π/5. Cool beans! In a perfect world, the formula to figure out the length of a radius given an arc length and central angle is:
Radius = (Arc Length) / (Central Angle)
Now, we just need to plug in the numbers and do some math magic.
Radius = (24π/5) / (3π/5)
Now, let's cancel out those pesky π's.
Radius = (24/5) / (3/5)
Ah, the glory of math when things start canceling out. So, let's simplify further.
Radius = 24/5 * 5/3
Now, it's time for some multiplication.
Radius = 8
There you have it, my friend! The length of the radius of the circle is 8 units. Ta-dah!
To find the length of the radius, you can use the formula:
Arc Length = radius * central angle
Given that the arc length is 24π/5 and the central angle is 3π/5, we can substitute these values into the formula:
24π/5 = radius * (3π/5)
To solve for the radius, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by (3π/5):
(24π/5) / (3π/5) = radius
Simplifying the equation:
(24π/5) * (5/3π) = radius
The π's cancel out:
(24/1) * (1/3) = radius
Multiplying and simplifying:
8 = radius
Therefore, the length of the radius is 8 units.
To find the length of the radius of a circle given the central angle and arc length, we can use the formula:
arc length = radius * central angle
In this case, we have the arc length as 24π/5 and the central angle as 3π/5. Let's substitute these values into the formula and solve for the radius.
24π/5 = radius * 3π/5
To solve for the radius, we can cancel out the π/5 terms on both sides of the equation:
24 = radius * 3
Now, divide both sides of the equation by 3 to isolate the radius:
radius = 24/3
radius = 8
Therefore, the length of the radius of the circle is 8 units.