A chord 30cm long is 20cm from the center of the circle. Calculate the length of the circle which is 24cm from the center
8cm
To calculate the length of the circle, we first need to determine the radius.
Given:
Length of chord (c) = 30 cm
Distance of chord from the center of the circle (d) = 20 cm
To find the radius (r), we can use the formula:
r = √(d^2 + (c/2)^2)
Substituting the given values:
r = √(20^2 + (30/2)^2)
r = √(400 + 225)
r = √625
r = 25 cm
Now that we know the radius, we can calculate the length of the circle.
The length of a circle is given by the formula:
C = 2πr
Substituting the value of the radius:
C = 2π(25)
C = 50π cm
To calculate the length, we substitute the value of π (pi) as approximately 3.14:
C ≈ 50(3.14)
C ≈ 157 cm
Therefore, the length of the circle which is 24 cm from the center is approximately 157 cm.
To calculate the length of a circle, we can use the formula for the circumference of a circle. The formula is C = 2πr, where C is the circumference and r is the radius of the circle.
In this case, we are given the length of a chord (30 cm) and the distance of that chord from the center of the circle (20 cm).
To find the radius of the circle, we need to draw a radius perpendicular to the chord. This will bisect the chord into two equal parts.
Since the length of the chord is 30 cm and it is bisected by the radius, each half of the chord will be 15 cm.
Now, we can use the Pythagorean theorem to find the radius of the circle. The theorem states that in a right-angled triangle, the square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides (a^2 + b^2).
In this case, one side of the right-angled triangle is half the length of the chord (15 cm), and the other side is the distance from the center to the chord (20 cm). Let's call the radius of the circle (r).
We can set up the equation: r^2 = 15^2 + 20^2.
Simplifying this equation, we get: r^2 = 225 + 400.
Combine the terms: r^2 = 625.
Taking the square root of both sides, we have: r = √625.
Simplifying, we get: r = 25.
Now that we have the radius (r = 25 cm), we can calculate the circumference using the formula C = 2πr.
Substituting the value of r, we get: C = 2π(25).
Simplifying further, we have: C = 50π.
Therefore, the length of the circle, which is 24 cm from the center, is 50π cm.
Draw a diagram. It should be easy to see that the radius is 25cm.
For this circle, no part of the circle is 24cm from the center.
However, a chord which is 24cm from the center subtends an angle θ such that cos(θ/2) = 24/25
The arc subtended by this angle is thus s = rθ = 25*2arccos(24/25) ≈ 14.19