What is the difference between the circumference and diameter of a circle?

Circumference vs Diameter vs Radius

Radius, diameter, and circumference are measurements of three important properties of a circle.

Diameter and Radius

A circle is defined as the locus of a point at a constant distance from a fixed point on a two dimensional plane. The fixed point is known as the center. The constant length is known as the radius. It is the shortest distance between the center and the locus. A line segment starting from the locus passing through the center and end on the locus is known as the diameter.

The radius and the diameter are important parameters of a circle because they determine the size of the circle. To draw a circle, either radius or diameter is only required.

Diameter and radius are mathematically related by the following formula

D = 2r

where D is the diameter and r is the radius.

Circumference

The locus of the point is known as the circumference. Circumference is a curved line, and its length is dependent on the radius or the diameter. The mathematical relation between radius (or diameter) and circumference is given by the following formula:

C = 2πr = πD

Where C is the circumference and π=3.14. The Greek letter pi (π) is a constant and important in many mathematical and physical systems. It is an irrational number and has the value 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679…… In most cases the value of pi up to two decimal places, i.e. π=3.14, is sufficient for considerable accuracy.

Often, in intermediate level school mathematics, above formula is used to define the constant pi (π) as the ratio between the diameter of a circle and its circumference, where its value is approximately given as the fraction 22/7.

What is the difference between Circumference, Radius, and Diameter?

• Radius and diameter are straight lines while circumference is a closed curve.

• Diameter is twice as the radius.

• Circumference is 2π times the radius of the circle or π times the diameter of the circle.

Answer

Verified

Hint: The diameter of a circle is double the radius of a circle. As a result, diameter is written as 2r. Similarly, we know that the circumference of a circle is equal to \[2\pi r\] . Given that the difference between the perimeter and the diameter of the object is 15 m, we get \[2\pi r-2r=15\,m\] . Solve the above equation to get the value of r. then substitute in the formula of area of circle and get the answer.

Complete step-by-step answer:

Here in this figure, to find the area first of all we need to find the radius for that we need to use the \[d=2r\] and circumference is the perimeter of the circle that means a measure of the outer round length of the circle. But it is given in the question that the difference between circumference and diameter of a circle is 15 cm then, we have to find the radius of the circle is r. then we know that the diameter of the circle is double the radius. So, the value diameter can be given as \[2\times radius\] .We get the diameter of a circle \[=2r\] Now, we know that the circumference of a circle is given by the formula \[2\pi r\] . Given the difference between circumference and diameter of a circle is 15 cm, which clearly means that the difference \[2\pi r\] and \[2r\] is 15 m. then we get: \[2\pi r-2r=15m----(1)\] Take 2r common on LHS, we get: \[2r(\pi -1)=15\] , substituting the value of \[\pi \] as \[\dfrac{22}{7}\] , we get: \[\Rightarrow 2r\left( \dfrac{22}{7}-1 \right)=15\] By simplifying further, we get: \[\Rightarrow 2r\left( \dfrac{22-7}{7} \right)=15\] Multiply 7 on both side and further solving we get: \[\Rightarrow 2r\left( 15 \right)=15\times 7\] By simplification we get: \[\Rightarrow 30r=105\] Therefore, we get the value of r from above equation we get: \[\Rightarrow r=\dfrac{105}{30}\] \[\Rightarrow \therefore r=3.5\,m\] As we know that Area of a circle is \[\pi \,{{r}^{2}}\] we have to substitute the value of r in this formula we get: \[A=\dfrac{22}{7}\,\times {{(3.5)}^{2}}\] After simplifying we get \[A=\dfrac{22}{7}\,\times (12.5)\] Further solving this we get: \[A=38.5\,{{m}^{2}}\] So, the correct option is “option C”.

So, the correct answer is “Option C”.

Note: To answer the circle question, one needs to understand the radius, diameter, circumference, and area of a circle, as well as how to compute the area of a circle. When estimating the area of a circle, there are a few things to keep in mind. First, see which value of \[\pi \] , which is 3.14 and \[\dfrac{22}{7}\] will give you the simplest solution and help in the calculation.

Updated April 24, 2017

By Rebecca Smith

In geometry, the terms circumference and diameter refer to the length of specific parts of a circle. They are two different measurements of length, but they share a special mathematical relationship with the constant pi.

The diameter is the length, or distance, across the circle at its widest point, passing through the center. Another related measurement, the radius, is a line that goes from the center to the circle's edge. The diameter is equal to 2 times the radius. (A line that goes across the circle, but not at its widest point, is called a chord.)

The circumference is the perimeter, or distance around the circle. Imagine wrapping a string all the way around a circle. Now imagine removing the string and pulling it out into a straight line. If you were to measure this string, that length is the circumference of your circle.

The quantity pi is a mathematical constant defined as the ratio of a circle's circumference to its diameter. This ratio is always the same. If you divide the circumference of any circle by its diameter, you always get pi. Mathematicians use the number 3.14 when using pi in calculations.

If you know a circle's diameter, you can calculate its circumference with this equation: Circumference = diameter times pi (3.14).