The diameter of a circle is 14 inches. What is the circle’s area
use 3.14 for PI
The Correct Answer and Explanation is:
To find the area of a circle, we use the formula:
[
\text{Area} = \pi \times r^2
]
where ( \pi ) (pi) is approximately 3.14, and ( r ) represents the radius of the circle. The radius is half of the diameter, so if the diameter of the circle is given as 14 inches, we can find the radius by dividing the diameter by 2:
[
r = \frac{14}{2} = 7 \text{ inches}
]
Now, substitute the values of ( \pi ) and ( r ) into the area formula:
[
\text{Area} = 3.14 \times (7)^2
]
First, calculate ( 7^2 ):
[
7^2 = 49
]
Then multiply by ( \pi ):
[
\text{Area} = 3.14 \times 49 = 153.86 \text{ square inches}
]
So, the area of the circle is 153.86 square inches.
Explanation
The area of a circle represents the amount of space within its boundary, and it is measured in square units (in this case, square inches). To determine the area, we need to understand two key measurements: the diameter and the radius. The diameter is the total width of the circle passing through its center, while the radius is half of that distance, extending from the center to any point on the circle’s edge.
In this problem, the diameter of the circle is given as 14 inches, so the radius is half of that, or 7 inches. Using the radius in the formula for the area of a circle, ( \pi \times r^2 ), allows us to determine the total square inches within the circle’s boundaries. Here, squaring the radius (7 inches) gives 49, which represents the radius’s effect in two-dimensional space (length and width). Multiplying by ( \pi ) (3.14) then scales this squared measurement to account for the circular shape, providing an accurate area.
This concept is fundamental in geometry and essential for various practical applications, from designing circular objects to calculating materials needed for circular surfaces.