2.Find the length of the arc in a circle if the radius of the circle is 24cm and the degree of the arc is 90o
3.Find the length of the arc if a circle if the degree if the arc is 120o and the length of the radius is 8cm.
4. A circle has a radius of 7. Find the diameter (D) and the (A).
5. Find the circumferemce of a circle if the area is 9/25pift^2.
#1 and #2 are the same type of problem
I will do #2
whole circumference = 2π(8) = 16π
but 120° is 1/3 of the circle, thus the arc is 1/3 the circumference
= (1/3)(16π) = 16π/3 cm or appr 16.755 cm
#4 ??? come on now!!!
#5 area = πr^2
πr^2 = (9/25)π
r^2 = 9/25
r = 3/5
circumf = 2πr = 2π(3/5) = 6π/5 ft or appr. .....
2. To find the length of an arc in a circle, you can use the formula: L = (θ/360) * 2πr, where L is the length of the arc, θ is the degree measure of the arc, π is a constant (approximately 3.14), and r is the radius of the circle.
For this problem, the radius (r) is given as 24 cm and the degree (θ) is given as 90°.
Plugging these values into the formula:
L = (90/360) * 2π * 24
Simplifying:
L = (1/4) * 2π * 24
L = π * 12
L = 12π cm
Therefore, the length of the arc is 12π cm.
3. Using the same formula, we can find the length of the arc in this problem. The degree of the arc is given as 120° and the radius (r) is given as 8 cm.
Plugging these values into the formula:
L = (120/360) * 2π * 8
Simplifying:
L = (1/3) * 2π * 8
L = (2/3) * π * 8
L = 16π/3 cm
Therefore, the length of the arc is 16π/3 cm.
4. To find the diameter (D) of a circle, you can double the radius (r). In this problem, the radius is given as 7. So, the diameter (D) would be:
D = 2 * 7
D = 14 units
Therefore, the diameter of the circle is 14 units.
To find the area (A) of a circle, you can use the formula: A = π * r^2, where A is the area and r is the radius.
In this problem, the radius is given as 7. Plugging this into the formula:
A = π * 7^2
A = π * 49
A = 49π square units
Therefore, the area of the circle is 49π square units.
5. To find the circumference of a circle, you can use the formula: C = 2πr, where C is the circumference and r is the radius.
In this problem, the area of the circle is given as 9/25π ft^2. The formula for the area of a circle is: A = πr^2.
So, we have: 9/25π = πr^2
To find the radius (r), we can rearrange this equation: r^2 = (9/25)
Taking the square root of both sides, we get: r = √(9/25) = 3/5
Now, we can find the circumference (C) using the formula:
C = 2π * (3/5)
Simplifying:
C = (6/5)π
Therefore, the circumference of the circle is (6/5)π ft.