Question

A glass window is in the shape of a semicircle with dimensions shown.
1.2 meters
What is the approximate perimeter of the window? (Use 3.14 as an approximation for PI.)
A.1.9 meters
B.3.1 meters
C.3.8 meters
D.5 meters

Answer 1

To calculate the perimeter of the semicircular window, we need to consider both the curved portion (the semicircle) and the straight portion (the diameter).

1. **Finding the curved length of the semicircle:**
- The radius \( r \) of the semicircle is half of the diameter. Given that the diameter is 1.2 meters, the radius is:
\[
r = \frac{1.2}{2} = 0.6 \text{ meters}
\]
- The formula for the circumference \( C \) of a full circle is:
\[
C = 2 \pi r
\]
- Therefore, the length of the semicircle is half of the circumference:
\[
\text{Length of semicircle} = \frac{1}{2} \times 2 \pi r = \pi r = 3.14 \times 0.6 \approx 1.884 \text{ meters}
\]

2. **Length of the straight edge (diameter):**
- The straight edge is simply the diameter, which is:
\[
\text{Diameter} = 1.2 \text{ meters}
\]

3. **Total perimeter of the window:**
- Finally, we sum the length of the curved edge and the diameter:
\[
\text{Perimeter} = \text{Length of semicircle} + \text{Diameter} = 1.884 + 1.2 \approx 3.084 \text{ meters}
\]

Now, rounding 3.084 meters gives us approximately 3.1 meters.

So, the answer is **B. 3.1 meters.**