Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona's circle?
A. [tex]$7 \pi m^2$[/tex]
B. [tex]$14 \pi m^2$[/tex]
C. [tex]$28 \pi m^2$[/tex]
D. [tex]$49 \pi m^2$[/tex]
Answer (2)
Find the radius by dividing the diameter by 2: r = 2 14 = 7 meters.
Calculate the area using the formula A = π r 2 .
Substitute the radius into the formula: A = π ( 7 2 ) = 49 π square meters.
The area of Fiona's circle is 49 π m 2 .
Explanation
Problem Analysis Let's analyze the problem. We are given the diameter of a circle and asked to find its area. The formula for the area of a circle is A = π r 2 , where r is the radius of the circle. We know that the radius is half of the diameter.
Calculate the Radius First, we need to find the radius of the circle. The diameter is given as 14 meters. So, the radius r is: r = 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 = π r 2 :
A = π ( 7 2 ) = π ( 49 ) = 49 π square meters
Final Answer Therefore, the area of Fiona's circle is 49 π square meters.
Examples
Circles are everywhere! Imagine you're planting a circular flower bed in your garden. Knowing the diameter helps you calculate the area you'll need to cover with soil and how many plants you can fit in the space. If the flower bed has a diameter of 14 meters, like Fiona's circle, you can calculate the area as A = π r 2 = π ( 7 2 ) = 49 π ≈ 153.94 square meters. This helps you plan your garden layout effectively!
The area of Fiona's circle is calculated to be 49 π square meters, using the formula A = π r 2 , where the radius is determined from the diameter. This corresponds to option D, 49 π m 2 .
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