Find the area of the sector of a circle of radius 7cm if the corresponding arc length is 6.2cm

To find the area of the sector of a circle, you need two pieces of information: the radius of the circle and the measure of the corresponding arc.

Let's start by finding the angle corresponding to the given arc length. The formula to calculate the angle of an arc is:

angle = (arc length / circumference) * 360°

To use this formula, we need to know the circumference of the circle. The circumference of a circle is given by:

circumference = 2 * π * radius

In this case, the radius is given as 7cm. So, we can find the circumference:

circumference = 2 * π * 7 cm
circumference = 14π cm

Now that we have the circumference, we can find the angle:

angle = (6.2 cm / 14π cm) * 360°

Simplifying this equation, we get:

angle = (0.44643) * 360°
angle ≈ 160.714°

Now, to find the area of the sector, we use the formula:

area of sector = (angle / 360°) * π * (radius^2)

Plugging in the values:

area of sector = (160.714° / 360°) * π * (7 cm)^2
area of sector ≈ (0.44643) * π * 49 cm²
area of sector ≈ 68.354 cm²

Therefore, the area of the sector of the circle with a radius of 7cm and an arc length of 6.2cm is approximately 68.354 cm².

To find the area of the sector of a circle, you need to know the radius and the central angle of the sector.

In this case, we are given the radius of 7 cm and the corresponding arc length of 6.2 cm. To find the central angle, we can use the formula:

angle = (arc length / circumference) * 360 degrees

First, let's calculate the circumference of the circle using the formula:

circumference = 2 * π * radius

circumference = 2 * 3.14 * 7
= 43.96 cm

Now, let's substitute the values into the formula to find the central angle:

angle = (6.2 / 43.96) * 360
= 0.1411 * 360
= 50.8 degrees

To calculate the area of the sector, we use the formula:

area = (central angle / 360 degrees) * π * radius^2

area = (50.8 / 360) * 3.14 * 7^2
= 0.1411 * 3.14 * 49
≈ 21.22 cm²

Therefore, the area of the sector is approximately 21.22 cm².

s = rθ, so

a = 1/2 r^2 θ = 1/2 * 49 * (6.2/7) = 21.7