Question

What will be the perimeter of semicircle of diameter of 14 cm ? (Take \(\pi = \frac{22}{7}\))

• A. 77 cm
• B. 28 cm
• C. 36 cm
• D. 22 cm

Hint:

For a semicircle of radius \(r = 7\text{ cm}\), the curved part is always \(22\text{ cm}\) (since \(\frac{22}{7} \times 7 = 22\)).
Simply add the diameter to this value: \(22 + 14 = 36\text{ cm}\).
This is a standard dimension combination that appears frequently.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question is from the topic of Mensuration, focusing on the boundary length (perimeter) of a 2D geometric shape, specifically a semicircle.

Step 2: Key Formula or Approach:
A semicircle consists of a curved boundary (half the circumference of a circle) and a straight flat boundary (the diameter of the circle).
Therefore, the perimeter (\(P\)) of a semicircle of radius \(r\) and diameter \(d\) is:
\[ P = \pi r + d \]
or, using radius \(r\):
\[ P = \pi r + 2r = r(\pi + 2) \]

Step 3: Detailed Explanation:
We are given:
Diameter of the semicircle, \(d = 14\text{ cm}\).
First, calculate the radius \(r\):
\[ r = \frac{d}{2} = \frac{14}{2} = 7\text{ cm} \]
Now, compute the length of the curved boundary (arc length):
\[ \text{Arc Length} = \pi r \]
Substitute \(\pi = \frac{22}{7}\) and \(r = 7\text{ cm}\):
\[ \text{Arc Length} = \frac{22}{7} \times 7 = 22\text{ cm} \]
Next, add the straight boundary (the diameter) to find the total perimeter:
\[ P = \text{Arc Length} + d \]
\[ P = 22 + 14 = 36\text{ cm} \]

Step 4: Final Answer:
The perimeter of the semicircle is \(36\text{ cm}\).