The Diameter Of A Circle Is 25 M. Find Its Area To The Nearest Whole Number.
Finding the area of a circle when given its diameter is a common mathematical problem. In this case, we are given that the diameter of the circle is 25 m. To find its area to the nearest whole number, we can use the formula for calculating the area of a circle.
The formula for finding the area of a circle is A = πr^2, where A represents the area and r represents the radius of the circle. Since we are given the diameter, which is twice the length of the radius, we can divide it by 2 to find our value for r.
So, if we have a diameter of 25 m, our radius would be 25/2 = 12.5 m. Plugging this value into our formula, we get A = π(12.5)^2.
To calculate it to the nearest whole number, let’s use an approximation for π as 3.14. Evaluating our expression gives us A ≈ 3.14(12.5)^2.
Simplifying further yields A ≈ 3.14 * 156.25 = 490.875 square meters.
Rounding this result to the nearest whole number gives us an approximate area of 491 square meters for a circle with a diameter of 25 meters.
Understanding The Formula For Finding The Area Of A Circle
Calculating the area of a circle is an essential skill in mathematics and geometry. The formula to determine the area of a circle is based on its diameter or radius. In this section, we’ll delve into understanding this formula and how it relates to finding the area of a circle when given its diameter.
To begin, let’s recap what the diameter represents. The diameter of a circle is defined as the distance across its widest point, passing through the center. In our case, we have a circle with a known diameter of 25 meters.
The formula for finding the area of a circle is A = πr², where A represents the area and r denotes the radius. To calculate using diameter instead of radius, we need to first find the radius by dividing the diameter by 2.
In our example, since we know that the diameter is 25 meters, we can easily find out that our radius would be half of that value: 25 / 2 = 12.5 meters.
Now that we have determined our radius (12.5 meters), we can substitute this value into our formula: A = π(12.5)². Simplifying further gives us A = π(156.25).
To find an approximate whole number for this area calculation, let’s use an approximation for pi (π). Taking pi as approximately equal to 3.14 will allow us to make an accurate estimation without excessive decimal places.
Plugging in this approximation yields A ≈ 3.14 * 156.25 = 490.625 square meters.
Rounding off to the nearest whole number gives us an estimated area of approximately 491 square meters.
Remember that when working with circles or any mathematical calculations involving approximations, it’s important to specify whether you require an exact answer or if estimates are acceptable within certain boundaries.
Understanding how to utilize the formula for finding the area of a circle, given its diameter, empowers us to confidently solve similar problems and deepen our understanding of geometric concepts.
Applying The Formula To Find The Radius
To find the area of a circle, we need to know its radius. In this case, we are given that the diameter of the circle is 25 meters. The formula for finding the radius of a circle when we know its diameter is simple: divide the diameter by 2.
So, if we have a circle with a diameter of 25 meters, we can find its radius by dividing 25 by 2. This gives us a radius of 12.5 meters. Now that we have the radius, we can move on to calculating the area.
The formula for finding the area of a circle is A = πr², where A represents the area and r represents the radius. In our case, since we know that our radius is 12.5 meters, we can substitute it into our formula:
A = π(12.5)²
Now let’s solve this equation step by step:
A = π(12.5)² A = π(156.25) A ≈ 490.87
Therefore, when rounding to the nearest whole number, the approximate area of this circle is 491 square meters.
It’s important to note that in this calculation I used an approximation for pi (π) as most practical calculations do not require high precision values for everyday use.
By applying these formulas correctly and understanding how they work together, you can easily find the area of any given circle when provided with its diameter or radius.
Remember to check your calculations and make sure you’ve used consistent units throughout your problem-solving process.
