What is the difference between circumference and circle?

Answer

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You Can Draw It Yourself
Remembering
Area Compared to a Square

Verified

Hint: In question it is given that the difference between the circumference and the radius of a circle is 37 cm and we have to find the diameter of a circle so what we will do is we will substitute the formula of circumference and radius r and solve the equation putting it equals to 37 cm.

Complete step-by-step solution:

The radius of a circle denoted by r is the distance of the line from the centre of the circle to the outer edge, and the circumference of a circle is the perimeter of the circle that means a measure of the outer round length of the circle.The formula to find the circumference is $2\pi r$, where $\pi $ is spelled as pi and is equal to $\dfrac{22}{7}$ or approximately equals to $3.14....$.Now, in question, it is given that the difference between the circumference and the radius of a circle is 37 cm and we have to find the diameter of a circle. The diameter of a circle is length equals to twice of the radius that is if d denotes diameter and r denotes radius, then d = 2r.So, as the difference between the circumference and the radius of a circle is 37 cm, then$2\pi r-r=37$Now, taking common factor which is r, outside$r(2\pi -1)=37$……………..... ( i ) Now, putting value of $\pi $equals to $\dfrac{22}{7}$ in equation ( i ), we get$r(2\cdot \dfrac{22}{7}-1)=37$On solving we get\[r(\dfrac{44}{7}-1)=37\]Taking L.C.M in brackets we get,\[r(\dfrac{44-7}{7})=37\]On solving, we get\[r(\dfrac{37}{7})=37\]Taking 7 from denominator on left hand side to numerator on right side we get, \[r\times 37=37\times 7\]On solving we get,\[r=7\]So, the radius is equal to 7 cm.Now, as the discussed diameter of a circle is twice the radius of a circleSo, the diameter of circle \[=2\times r\]……………..…( ii )Putting the value of r in equation ( ii ), we get\[2\times 7=14\] cmHence, the diameter of the circle equals 14 cm.

Hence, option ( b ) is correct.

Note: While solving the questions of the circle, one must know the concept of the radius of a circle, the diameter of circle and circumference of the circle, and how to calculate the circumference of the circle. While calculating circumference first see which value of $\pi $, which are 3.14 and $\dfrac{22}{7}$ will give you the most simplest solution and help in the calculation.

A circle is easy to make:

Draw a curve that is "radius" away
from a central point.

And so:

All points are the same distance from the center.

You Can Draw It Yourself

Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!

images/circle-prop.js?mode=radius

Try dragging the point to see how the radius and circumference change.

(See if you can keep a constant radius!)

The Radius is the distance from the center outwards.

The Diameter goes straight across the circle, through the center.

The Circumference is the distance once around the circle.

And here is the really cool thing:

When we divide the circumference by the diameter we get 3.141592654...
which is the number π (Pi)

So when the diameter is 1, the circumference is 3.141592654...

We can say:

Circumference = π × Diameter

Distance walked = Circumference = π × 100m

= 314m (to the nearest m)

Also note that the Diameter is twice the Radius:

Diameter = 2 × Radius

And so this is also true:

Circumference = 2 × π × Radius

In Summary:

Remembering

The length of the words may help you remember:

Radius is the shortest word and shortest measure
Diameter is longer
Circumference is the longest

Definition

The circle is a plane shape (two dimensional), so:

Area

The area of a circle is π times the radius squared, which is written:

A = π r2

Where

A is the Area
r is the radius

To help you remember think "Pie Are Squared" (even though pies are usually round):

Area= πr2

= π × 1.22

= 3.14159... × (1.2 × 1.2)

= 4.52 (to 2 decimals)

Or, using the Diameter:

A = (π/4) × D2

Area Compared to a Square

A circle has about 80% of the area of a similar-width square.
The actual value is (π/4) = 0.785398... = 78.5398...%

And something interesting for you to try: Circle Area by Lines

Names

Because people have studied circles for thousands of years special names have come about.

Nobody wants to say "that line that starts at one side of the circle, goes through the center and ends on the other side" when they can just say "Diameter".

So here are the most common special names:

Lines

A line that "just touches" the circle as it passes by is called a Tangent.

A line that cuts the circle at two points is called a Secant.

A line segment that goes from one point to another on the circle's circumference is called a Chord.

If it passes through the center it is called a Diameter.

And a part of the circumference is called an Arc.

There are two main "slices" of a circle.

The "pizza" slice is called a Sector.

And the slice made by a chord is called a Segment.

The Quadrant and Semicircle are two special types of Sector:

Quarter of a circle is called a Quadrant.

Half a circle is called a Semicircle.

A circle has an inside and an outside (of course!). But it also has an "on", because we could be right on the circle.

Example: "A" is outside the circle, "B" is inside the circle and "C" is on the circle.

Ellipse

A circle is a "special case" of an ellipse.

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Activity: Approximate Value For Pi

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).