To understand the problem, we need to know what a circle is and what its circumference and area represent. A circle is a perfectly round shape with all points equidistant from the center. The circumference of a circle is the distance around its outer edge, while the area of a circle is the measure of the space enclosed by the circle.
The problem asks us to find the area of a circle with a given circumference of 31.4 units.
The answer to the problem is the area of the circle.
There are different methods to solve this problem depending on the information given. We will discuss three methods:
To calculate the area of a circle with a circumference of 31.4 units, we can use Method 3 since the circumference is given.
List the formulas for calculating the area and circumference of a circle:
Plug the circumference of the circle into the formula for circumference: 31.4 = 2πr
Solve for the radius (r): Divide both sides of the equation by 2π: r = 31.4 / (2π)
Finally, calculate the area using the formula for the area of a circle: A = πr^2 Substitute the value of r: A = π * (31.4 / (2π))^2
Simplify the expression: A = π * (31.4^2 / (2π)^2) A = π * (31.4^2 / 4π^2) A = (31.4^2 / 4π)
Calculate the value of the expression using a calculator: A ≈ 246.3 square units
Therefore, the area of a circle with a circumference of 31.4 units is approximately 246.3 square units.
A circle is a two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed center point. It is perfectly round and has no corners or edges.
To draw a circle, you can use a compass, which is a tool with two arms. One arm has a sharp point, and the other arm has a pencil or pen attached. Place the sharp point at the center of the circle and rotate the compass around it, keeping the pencil or pen in contact with the paper. This will create a perfect circle.
A circle has several important measurements:
The symbol Π (pi) represents the mathematical constant that is the ratio of the circumference of any circle to its diameter. It is an irrational number, approximately equal to 3.14159. Pi is used in many mathematical formulas involving circles and is a fundamental constant in mathematics.
The origin of the symbol Π (pi) can be traced back to ancient Greece. The Greek mathematician Archimedes is often credited with the first accurate calculation of pi. The symbol Π was later introduced by the Welsh mathematician William Jones in 1706, who used it to represent the ratio of the circumference to the diameter of a circle.
Question: Calculate the area of a circle with a circumference of 31.4 units.
To calculate the area of a circle with a circumference of 31.4 units, we can use the formula A = πr^2. By solving the equation step by step, we find that the area is approximately 246.3 square units.