Question
A glass window is in the shape of a semicircle with dimensions shown.
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
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
Answers
GPT-4o mini
To find the perimeter of a semicircular window, we need to calculate two parts: the curved part (which is half the circumference of a full circle) and the straight part (the diameter of the semicircle).
Let's use the formula for the circumference of a circle, which is given by:
\[ C = 2\pi r \]
Where \( r \) is the radius of the circle. Since we are dealing with a semicircle, we will take half of the circumference:
\[ \text{Curved part} = \frac{1}{2} C = \frac{1}{2} (2\pi r) = \pi r \]
The diameter, which is the straight part of the perimeter, is given by:
\[ d = 2r \]
Now, the total perimeter \( P \) of the semicircular window can be calculated as:
\[ P = \text{Curved part} + \text{Diameter} \]
Substituting the values, we have:
\[ P = \pi r + 2r \]
Now, let's determine the perimeter based on the radius. However, since the problem doesn't specify the radius, let’s assume a radius \( r \) = 1 meter (a common assumption unless specified).
1. Calculate the curved part:
- \( \text{Curved part} = \pi r = 3.14 \times 1 = 3.14 \) meters.
2. Calculate the diameter:
- \( \text{Diameter} = 2r = 2 \times 1 = 2 \) meters.
Now, plug these values into the perimeter equation:
\[ P = 3.14 + 2 \]
\[ P = 5.14 \text{ meters} \]
Now since this scenario may differ depending on the value of \( r \) specified in the problem, and with regards to the options available:
A. 1.9 meters
B. 3.1 meters
C. 3.8 meters
D. 5 meters
Considering it leads to approximately 5 meters and the measurements might be rounded, the best estimate of the perimeter here would be:
**D. 5 meters**
Let's use the formula for the circumference of a circle, which is given by:
\[ C = 2\pi r \]
Where \( r \) is the radius of the circle. Since we are dealing with a semicircle, we will take half of the circumference:
\[ \text{Curved part} = \frac{1}{2} C = \frac{1}{2} (2\pi r) = \pi r \]
The diameter, which is the straight part of the perimeter, is given by:
\[ d = 2r \]
Now, the total perimeter \( P \) of the semicircular window can be calculated as:
\[ P = \text{Curved part} + \text{Diameter} \]
Substituting the values, we have:
\[ P = \pi r + 2r \]
Now, let's determine the perimeter based on the radius. However, since the problem doesn't specify the radius, let’s assume a radius \( r \) = 1 meter (a common assumption unless specified).
1. Calculate the curved part:
- \( \text{Curved part} = \pi r = 3.14 \times 1 = 3.14 \) meters.
2. Calculate the diameter:
- \( \text{Diameter} = 2r = 2 \times 1 = 2 \) meters.
Now, plug these values into the perimeter equation:
\[ P = 3.14 + 2 \]
\[ P = 5.14 \text{ meters} \]
Now since this scenario may differ depending on the value of \( r \) specified in the problem, and with regards to the options available:
A. 1.9 meters
B. 3.1 meters
C. 3.8 meters
D. 5 meters
Considering it leads to approximately 5 meters and the measurements might be rounded, the best estimate of the perimeter here would be:
**D. 5 meters**