What is the perimeter & area of the sector with 100 degrees angle and radius of 20cm?
To find the perimeter and area of a sector, you need to know its angle and radius. Here's how you can calculate the perimeter and area of the sector with a 100 degrees angle and a radius of 20 cm:
1. Perimeter of a sector:
- The perimeter of a sector is the length of the curved boundary of the sector.
- To find the perimeter of a sector, you need to calculate the circumference of the circle and then multiply it by the ratio of the sector's angle to 360 degrees.
The circumference of a circle with a given radius can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius.
In this case, the angle of the sector is 100 degrees, and the radius is 20 cm.
To calculate the perimeter, follow these steps:
1. Convert the angle from degrees to radians:
- 1 degree = π/180 radians
- 100 degrees = (100 × π) / 180 radians
- Convert this value to decimal form if necessary.
2. Calculate the circumference of the circle:
- C = 2πr
- C = 2 × π × 20 cm
3. Calculate the perimeter of the sector:
- Perimeter = C × (angle/360)
- Perimeter = (2 × π × 20 cm) × [(100 × π) / 180 / 360]
- Simplify the expression and calculate the value.
2. Area of a sector:
- The area of a sector is a fraction of the total area of a circle.
- To find the area of a sector, you need to calculate the area of the entire circle and then multiply it by the ratio of the sector's angle to 360 degrees.
The area of a circle with a given radius can be calculated using the formula: A = πr^2, where A is the area and r is the radius.
To calculate the area of the sector, follow these steps:
1. Calculate the area of the circle:
- A = πr^2
- A = π × (20 cm)^2
2. Calculate the area of the sector:
- Area = A × (angle/360)
- Area = (π × (20 cm)^2) × [(100 × π) / 180 / 360]
- Simplify the expression and calculate the value.
Once you follow these steps, you will have the perimeter and area of the sector with a 100 degrees angle and a radius of 20 cm.
the perimeter is two radii plus a section of the circumference
... the circumference section is ... 2 * π * r * (100 / 360)
the area is 100/360 of the whole circle ... π * r^2 * (100 / 360)