Question

The perimeter of a quadrant of a circle is 71.4cm. Find its area ​

Answer 1

circle: 6490.9 cm², quadrant: 1622.7 cm²

Explanation:

The circumference of the entire circle is known as 2πr and it is 4 times the given value, since a circle has 4 quadrants:

2πr = 4·71.4 = 285.6, so r = 285.6 / 2π ≈ 45.45

The area of a circle is πr², filling in the value for r we just found:

πr² = π 45.45² ≈ 6490.9 cm²

So the area of a quadrant is one fourth of that:

6490.9/4 = 1622.7 cm²

The question about "its area" can denote the entire circle, or just the quadrant, so two answers are provided.

Answer 2

Area = 1256 cm²

Explanation:

`\textsf{Perimeter of a quadrant of a circle}=\left((\pi)/(2)+2\right)r`

`\textsf{(where r is the radius)}`

Given:

• Perimeter = 71.4 cm
• π = 3.14

Substitute the given value into the equation and solve for r:

`\implies 71.4=\left((3.14)/(2)+2\right)r`

`\implies 71.4=3.57r`

`\implies r=(71.4)/(3.57)`

`\implies r=20`

Therefore, the radius of the circle is 20 cm

`\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}`

Substituting the found value of r into the equation and solving for A:

`\implies A=3.14(20)^2`

`\implies A=1256`

Therefore, the area of the circle is 1256 cm²