Question

A door with width 4.20 has an arc as shown in the diagram. Find: a the radius of the arc, to the nearest cm b the length of the arc, to the nearest cm. 225° is the central angle​

Answer 1

To find the radius of the arc, divide the circumference by π. To find the length of the arc, multiply the circumference by the central angle divided by 360°.

Step-by-step explanation:

To find the radius of the arc, we can use the formula:

a = c / π

where a is the central angle in degrees, and c is the circumference of the circle.

Given that the central angle is 225°, we can calculate the radius by substituting the values into the formula:

a = 225 / 360 * 2 * π * r

225 / 360 * 2 * π * r = 4.20

Simplifying the equation, we get:

r ≈ 4.20 / (225 / 360 * 2 * π)

r ≈ 1.89 cm

To find the length of the arc, we can use the formula:

l = c * (a / 360)

Substituting the values into the formula:

l = 2 * π * r * (225 / 360)

l ≈ 2 * π * 1.89 * (225 / 360)

l ≈ 7.46 cm