A semicircle has a diameter of 14 cm. What is the area of the semicircle?

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Question: A semicircle has a diameter of 14 cm. What is the area of the semicircle?

Options:

Correct Answer: 77 cm²

Solution:

Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = (1/2) × 3.14 × 49 = 76.96 cm², which rounds to 77 cm².

A semicircle has a diameter of 14 cm. What is the area of the semicircle?

A semicircle has a diameter of 14 cm. What is the area of the semicircle?

Step 1: Identify the diameter of the semicircle, which is given as 14 cm.
Step 2: Calculate the radius of the semicircle. The radius is half of the diameter, so divide 14 cm by 2. This gives you a radius of 7 cm.
Step 3: Use the formula for the area of a semicircle, which is (1/2) × π × r².
Step 4: Substitute the radius into the formula. So, it becomes (1/2) × π × (7 cm)².
Step 5: Calculate (7 cm)², which is 49 cm².
Step 6: Now substitute this value back into the formula: Area = (1/2) × π × 49 cm².
Step 7: Use the approximate value of π as 3.14. So, the area becomes (1/2) × 3.14 × 49 cm².
Step 8: Calculate (1/2) × 3.14, which is 1.57.
Step 9: Now multiply 1.57 by 49 cm². This gives you 76.93 cm².
Step 10: Round 76.93 cm² to the nearest whole number, which is 77 cm².

Area of a Semicircle – The area of a semicircle is calculated using the formula (1/2) × πr², where r is the radius.
Understanding Diameter and Radius – The radius is half of the diameter, which is crucial for correctly applying the area formula.