The radius of a semi circle is 21 cm. Find perimeter of semicircle
The correct answer and explanation is:
The radius of the semicircle is given as 21 cm. To find the perimeter of the semicircle, it is important to understand what the perimeter includes.
A semicircle is half of a full circle. Its perimeter consists of two parts:
- The curved edge, which is half the circumference of a full circle.
- The straight edge, which is the diameter of the circle.
First, recall the formula for the circumference of a full circle:
Circumference = 2 × π × radius
For a semicircle, the curved part is half the circumference:
Curved length = (1/2) × 2 × π × radius = π × radius
Next, the straight edge of the semicircle is the diameter:
Diameter = 2 × radius
Now, to find the total perimeter (P) of the semicircle, add the curved length and the diameter:
P = π × radius + 2 × radius
Given the radius is 21 cm, substitute the value into the formula:
P = π × 21 + 2 × 21
Using the value of π ≈ 3.1416:
P = 3.1416 × 21 + 42
P = 65.9736 + 42
P = 107.9736 cm
Rounded to two decimal places, the perimeter is approximately:
P ≈ 107.97 cm
In conclusion, the perimeter of the semicircle with radius 21 cm is about 107.97 cm.
Explanation
The perimeter of a semicircle is not just the half-circle curved edge but also includes the straight line connecting the endpoints of the curve, which is the diameter. The curved edge length comes from half the circumference because the semicircle is exactly half a circle. Adding the diameter completes the perimeter since the boundary of the semicircle is composed of these two parts. Substituting the given radius and using the value of π allows calculation of the numeric perimeter. This formula applies to any semicircle as long as the radius is known.