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 = 2 14 = 7 .
Apply the formula for the area of a circle: A = π r 2 .
Substitute the radius into the formula: A = π ( 7 2 ) = 49 π .
State the final answer: 49 π m 2 .
Explanation
Problem Analysis We are given a circle with a diameter of 14 meters. Our goal is to find the area of this circle.
Calculate the Radius The radius of a circle is half of its diameter. Therefore, the radius r of Fiona's circle is: r = 2 d iam e t er = 2 14 = 7 meters
State the Area Formula The area A of a circle is given by the formula: A = π r 2 where r is the radius of the circle.
Calculate the Area Now, substitute the value of the radius r = 7 meters into the area formula: A = π ( 7 ) 2 = 49 π m 2
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 you have available for planting flowers. Knowing the diameter of your garden, you can easily find the radius and then use the area formula to determine the total planting area. This helps you plan your garden layout and purchase the right amount of plants and materials. For instance, if your circular garden has a diameter of 14 meters, its area is 49 π m 2 , which is approximately 153.94 square meters.
