Chapter 1: Problem 64
What is the area of a circle of radius \(24.87 \mathrm{~m}\) ?
Short Answer
Expert verified
The area is approximately 1943.22 m².
Step by step solution
01
Formula for Area of a Circle
To find the area of a circle, we use the formula: \[ A = \pi r^2 \]where \( A \) is the area and \( r \) is the radius of the circle.
02
Substitute the Radius
Given that the radius \( r \) is \( 24.87 \) meters, we substitute it into the formula:\[ A = \pi (24.87)^2 \]
03
Calculate the Area
First, compute \( (24.87)^2 \):\[ (24.87)^2 = 618.5569 \]Now, substitute back to find \( A \):\[ A = \pi \times 618.5569 \]
04
Calculate Final Area Value
To calculate \( A \), multiply \( 618.5569 \) by \( \pi \) (approximately \( 3.14159 \)):\[ A \approx 3.14159 \times 618.5569 \approx 1943.2229 \]Therefore, the area is approximately \( 1943.22 \mathrm{~m}^2 \).
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Geometry
Geometry is the branch of mathematics that deals with shapes, sizes, and properties of space. It includes numerous concepts, such as points, lines, surfaces, and solids. Geometry is essential for understanding the world around us, as it is all about the physical space we live in. In this particular problem, we are dealing with the geometry of circles. Circles are fascinating shapes that have equal distances from a central point to all points on their outline, known as the boundary. This equal distance is called the radius. Understanding geometry helps you not only solve mathematical problems but also to grasp more complex concepts in a visual and practical way. Circles, in geometric terms, are two-dimensional shapes with a flat surface. The calculation of the area of a circle is a fundamental exercise in geometry, allowing us to apply the concepts of space and measurement in practical scenarios.
Radius of a Circle
The radius of a circle is one of its most important features. It is the straight-line distance from the center of the circle to any point on its boundary. Understanding the concept of a circle's radius is crucial when calculating its area.
- The radius helps us know the size of the circle, as larger radii mean larger circles.
- When you know the radius, you can also find other related measurements, like the circumference and diameter, using simple formulas.
- For instance, the diameter is twice the radius.
Mathematical Formulas
Mathematical formulas are tools that help us solve numerical problems by providing a set structure to follow. They turn complex problems into manageable steps.
- The formula to find the area of a circle is \( A = \pi r^2 \).
- In this formula, \( A \) represents the area, \( \pi \) is a constant approximately equal to 3.14159, and \( r \) is the radius of the circle.