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Perimeter and Area

Circles

Out of all the geometric shapes and figures, the circle is a fascinating form present around us. The pizza, coins, the sun are all circular in shape. Just a few important things in our lives that are circular in shape. And have you ever thought about how many sides a circle has or about the perimeter of a circle? Let us study what is a circle in detail.

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Circle

circle is a shape where all points have the same distance from the centre. Few real-world examples include a wheel, dining plate, coin etc. Drawing it properly isn’t easy with a running hand. The availability of a compass (a geometric tool) is preferred by most people, be it at school or at the workplace.

Perimeter of a Circle

Terms Related to Circle

Diameter

The diameter is a line which is drawn across a circle passing through the centre.

Radius

The distance from the middle or centre of a circle towards any point on it is a radius. Interestingly, when you place two radii back-to-back, the resultant would hold the same length as one diameter. Therefore, we can call one diameter twice as long as the concerned radius.

Chord

A line segment that joins two points present on a curve is the chord. In geometry, the usefulness of a chord is focused on describing a line segment connecting two endpoints which rest on a circle.

Tangent & Arc

A line which slightly touches the circle on its travel to a different direction is Tangent. On the other hand, a part of the circumference is an Arc.

Sector & Segment

A sector is a part of a circle surrounded by two radii of it together with their intercepted arc. The segment is that region which is enclosed by a chord together with the arc subtended by the chord.

Circumference or Perimeter of a Circle

Perimeter of a Circle

A perimeter of any geometrical figure is the length of the outer boundary of the shape. Similarly, in the case of a circle, the circumference would be the perimeter of a circle.

On practical grounds, let’s take an example of a wheel, the distance covered by the wheel in one complete revolution will be the circumference of the wheel. The formula for the circumference of a circle is,

C = 2πR

where C = circumference, R = Radius of the circle, π = It is constant pronounced as “pi” with a value of 22/7 or 3.14

Area of Circle

Area of any geometrical figure is the space occupied by it on a two-dimensional plane. Now, what is the area of a circle? Well, the area of a circle is the space occupied by it with a certain radius on a two-dimensional plane. So, if your parents want to put new carpet in your circular room, how much carpet you need to buy? Again, it will be equal to the area of the room.

Area of Circle = πR2

Properties of the Circle

  • Circles with equal radii are congruent.
  • Also, the circles with different radii appear to be similar.
  • The chords that are equidistant from the centre are of the same length.
  • All points on the circle are equidistant from the centre point.
  • The longest chord in the circle is the diameter.
  • A diameter of a circle divides it into two equal arcs. Each of the arcs is s a semi-circle.
  • If the radii of two circles are exactly the same value, then the circles are congruent.
  • Two or more circles that have different radii but the same centre are concentric circles.

Solved Example For You

Question 1. Find the area of a ring-shaped region enclosed between two concentric circles of radii 20 cm and 15 cm

  1. 550 cm²
  2. 500 cm²
  3. 750 cm²
  4. 950 cm²

Answer : A. Area of the shaded region = π (20²) – π (15²)
=  400 – 225 × 22/7
= 175 × 22/7
= 550 sq.cm

How can one calculate the perimeter of a circle?

Answer: A circle’s perimeter is called the circumference. The symbol of the circumference is C. One can calculate by making use of the formula PZi x diameter, or 3.14 x d = C.

Question 3: Explain what is the formula of semi-circle perimeter?

Answer: The circle’s circumference formula, C, is C = 2 * pi * r. A semicircle means half a circle. Therefore, in order to find the area of a semi-circle, one would need to divide the perimeter formula by two.

Question 4: Explain how one can find the length of the arc?

Answer: To find arc length, one must begin by undertaking division of the arc’s central angle in degrees by 360. Afterwards, one must multiply that number by the circle’s radius. Finally, there should be multiplication of that number by 2 × pi to find the arc length.

Question 5: What is the importance of the unit circle?

Answer: A unit circle is also known as the trig circle. The unit circle is important because one can easily calculate the tangent, sine, and cosine of any angle between 0° and 360°.

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