Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona's circle?
A. $7 \pi m^2$
B. $14 \pi m^2$
C. $28 \pi m^2$
D. $49 \pi m^2$
Answer (1)
Find the radius by dividing the diameter by 2: r a d i u s = 2 14 = 7 meters.
Calculate the area using the formula A re a = π ∗ r a d i u s 2 .
Substitute the radius into the formula: A re a = π ∗ ( 7 ) 2 .
The area of Fiona's circle is 49 π m 2 .
Explanation
Problem Analysis We are given a circle with a diameter of 14 meters. We need to find the area of this circle.
Calculate the Radius First, we need to find the radius of the circle. The radius is half of the diameter. So, we divide the diameter by 2: r a d i u s = 2 d iam e t er = 2 14 = 7 meters
Calculate the Area Now that we have the radius, we can calculate the area of the circle using the formula: A re a = π ∗ r a d i u s 2 Substituting the value of the radius: A re a = π ∗ ( 7 ) 2 = 49 π square meters
Final Answer Therefore, the area of Fiona's circle is 49 π square meters.
Examples
Imagine you're designing a circular garden and need to calculate how much area it will cover to buy the right amount of soil or fencing. Knowing the diameter, you can easily find the radius and then calculate the area using the formula A = π r 2 . This helps in planning and resource allocation for your garden project.
