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The circumference of a circle is 60π cm. What is the area of the circle to the nearest whole number?
The area of the circle is approximately 2827 square centimeters.
To find the area of a circle, you can use the formula:
A = πr^2
Where A is the area and r is the radius of the circle.
Given that the circumference of the circle is 60π cm, you can use the formula for circumference:
C = 2πr
Where C is the circumference and r is the radius.
From the given circumference 60π cm, you can solve for r:
60π = 2πr
Divide both sides by 2π:
r = 60π / 2π = 30
Now that you have the radius (r = 30), you can find the area (A) using the formula for the area of a circle:
A = π × 30^2 A = π × 900 A ≈ 2827
Rounding to the nearest whole number, the area of the circle is approximately 2827 square centimeters.
Circles and Circumference
A circle is a two-dimensional shape consisting of all points in a plane that are a given distance, called the radius, from a given point, called the center. The circumference of a circle is the distance around its outer edge.
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The formula to calculate the circumference of a circle is:
Circumference (C) = 2πr
Where:
- C is the circumference
- π (pi) is a mathematical constant approximately equal to 3.14159 (though in precise calculations, more decimal places are often used)
- r is the radius of the circle
Alternatively, you can also use the diameter (d) of the circle to find the circumference:
C = πd
Where:
- d is the diameter of the circle
These formulas allow you to find the circumference of any circle if you know either the radius or the diameter. It’s important to note that π is a constant value and is used in calculations involving circles and spheres.
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