Semi-Circle Calculator Form
About Semi-Circle Calculator
The Semi-Circle Calculator is an easy-to-use tool that calculates the diameter, circumference, and area of a semi-circle when you input its radius. This guide explains how to use the calculator, the formulas involved, detailed examples, and answers to frequently asked questions.
How to Use the Semi-Circle Calculator
To use the Semi-Circle Calculator, follow these steps:
- Step 1: Enter the Radius of the semi-circle.
- Step 2: Click on the Calculate button.
- Step 3: The calculator will display the Diameter, Circumference, and Area.
Formulas for Semi-Circle Calculator
Diameter (D)
The diameter (D) of a semi-circle is twice the radius.
\( D = 2 \times \text{Radius} \)
Circumference (C)
The circumference (C) of a semi-circle is the curved edge plus the straight edge (diameter).
\( C = \pi \times \text{Radius} + \text{Diameter} \)
Since \( \text{Diameter} = 2 \times \text{Radius} \), we can rewrite it as:
\( C = \pi \times \text{Radius} + 2 \times \text{Radius} = \text{Radius} \times (\pi + 2) \)
Area (A)
The area (A) of a semi-circle is half the area of a full circle.
\( A = \frac{1}{2} \times \pi \times \text{Radius}^2 \)
Examples
Example 1
Problem: Calculate the diameter, circumference, and area of a semi-circle with a radius of 4 units.
Solution
Step 1: Calculate the Diameter
Use the formula for diameter:
Diameter = 2 × Radius
Substitute the values:
Diameter = 2 × 4 = 8 units
Answer: The diameter of the semi-circle is 8 units.
Step 2: Calculate the Circumference
Use the formula for circumference:
Circumference = π × Radius + Diameter
Substitute the values (using π ≈ 3.14159):
Circumference = 3.14159 × 4 + 8 ≈ 20.57 units
Answer: The circumference of the semi-circle is approximately 20.57 units.
Step 3: Calculate the Area
Use the formula for area:
Area = ½ × π × Radius²
Substitute the values:
Area = 0.5 × 3.14159 × 4² ≈ 25.13 square units
Answer: The area of the semi-circle is approximately 25.13 square units.
Example 2
Problem: Calculate the diameter, circumference, and area of a semi-circle with a radius of 7 units.
Solution
Step 1: Calculate the Diameter
Use the formula for diameter:
Diameter = 2 × Radius
Substitute the values:
Diameter = 2 × 7 = 14 units
Answer: The diameter of the semi-circle is 14 units.
Step 2: Calculate the Circumference
Use the formula for circumference:
Circumference = π × Radius + Diameter
Substitute the values:
Circumference = 3.14159 × 7 + 14 ≈ 36.99 units
Answer: The circumference of the semi-circle is approximately 36.99 units.
Step 3: Calculate the Area
Use the formula for area:
Area = ½ × π × Radius²
Substitute the values:
Area = 0.5 × 3.14159 × 7² ≈ 76.97 square units
Answer: The area of the semi-circle is approximately 76.97 square units.
FAQs
1. How is the diameter of a semi-circle calculated?
The diameter of a semi-circle is twice the radius, calculated as \( D = 2 \times \text{Radius} \).
2. What is the formula for the circumference of a semi-circle?
The circumference of a semi-circle includes the curved edge and the diameter. It is calculated as \( C = \pi \times \text{Radius} + 2 \times \text{Radius} \).
3. How do I find the area of a semi-circle?
The area of a semi-circle is half the area of a full circle, calculated as \( A = ½ \times \pi \times \text{Radius}^2 \).