A circle has a diameter of 10 inches. what is the area of the circle?use 3.14 for pi
The Correct Answer and Explanation is :
To calculate the area of a circle, you can use the formula:
[
\text{Area} = \pi r^2
]
where ( \pi ) (pi) is a mathematical constant approximately equal to 3.14, and ( r ) is the radius of the circle.
Given that the diameter of the circle is 10 inches, you first need to find the radius. The radius is half of the diameter:
[
r = \frac{\text{diameter}}{2} = \frac{10 \, \text{inches}}{2} = 5 \, \text{inches}
]
Now that we have the radius, we can substitute it into the area formula. Using ( \pi = 3.14 ):
[
\text{Area} = 3.14 \times (5 \, \text{inches})^2
]
Calculating ( (5 \, \text{inches})^2 ):
[
(5 \, \text{inches})^2 = 25 \, \text{square inches}
]
Next, substituting this value back into the area formula:
[
\text{Area} = 3.14 \times 25 \, \text{square inches}
]
Calculating the multiplication:
[
3.14 \times 25 = 78.5 \, \text{square inches}
]
Thus, the area of the circle is:
[
\text{Area} = 78.5 \, \text{square inches}
]
In conclusion, the area of a circle can be easily calculated once you know the diameter. The relationship between diameter and radius is straightforward, and understanding these properties allows for quick calculations. Knowing that the radius is half of the diameter is crucial for using the area formula correctly. In real-life applications, such as designing circular objects or spaces, knowing how to calculate the area helps in determining the amount of material needed or the available space. Whether it’s for flooring, gardening, or crafting, the concept of area remains an essential aspect of geometry.