Length of tape required to cover the edges of a semicircular disc of radius 10 cm is

Options

A. 62.8 cm
B. 51.4 cm
C. 31.4 cm
D. 15.7 cm

Answer

To find the length of tape required to cover the edges of a semicircular disc with a radius of 10 cm, we will follow these steps:

### Step 1: Understand the shape
We have a semicircular disc, which means it is half of a full circle. The edges we need to cover include the curved edge and the straight edge (diameter).

### Step 2: Calculate the circumference of a full circle
The formula for the circumference (C) of a full circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 3: Calculate the circumference of the semicircle
Since we only need the curved part of the semicircle, we take half of the circumference of the full circle:
\[ \text{Curved part} = \frac{1}{2} \times 2\pi r = \pi r \]

### Step 4: Calculate the diameter of the semicircle
The diameter (d) of the semicircle is given by:
\[ d = 2r \]

### Step 5: Combine the lengths
To find the total length of tape required, we need to add the length of the curved part and the diameter:
\[ \text{Total Length} = \text{Curved part} + \text{Diameter} \]
\[ \text{Total Length} = \pi r + 2r \]

### Step 6: Substitute the radius
Now, substitute \( r = 10 \) cm into the equation:
\[ \text{Total Length} = \pi \times 10 + 2 \times 10 \]
\[ \text{Total Length} = 10\pi + 20 \]

### Step 7: Calculate the numerical value
Using \( \pi \approx 3.14 \):
\[ \text{Total Length} = 10 \times 3.14 + 20 \]
\[ \text{Total Length} = 31.4 + 20 \]
\[ \text{Total Length} = 51.4 \text{ cm} \]

### Final Answer
The length of tape required to cover the edges of the semicircular disc is **51.4 cm**.

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