7th Grade - Area of Circles

Introduction

  • A circle is a two-dimensional closed figure formed by joining a set of all the points equidistant from a fixed point.
  • The fixed point is called the circle's center, and the fixed distance is called the circle's radius.

  • The most extended chord that passes through the center of a circle joining the two points on the circumference of a circle, is called its diameter.

d=2r, where d=diameter of the circle & r=radius of the circle.

  • The circumference of a circle is the length of the boundary of a circle, and can be calculated using the formula C=2πr, where r=radius of the circle.

Area of Circles

  • The area of a circle is the measure of the region enclosed inside it.
  • The area of a circle depends on the length of its radius.
  • If we know the radius of a circle, we can calculate its area using the formula mentioned below.

Areacircle=π·r2, where π=2273.14, and r=the radius of the circle.

  • Likewise, if the diameter of a circle is known, its area can be calculated using the formula mentioned below.

Areacircle=π4·d2, where d=the diameter of the circle d=2r

Solved Examples

Example 1: What is the area of a circle with a radius of 7 cm?

Solution: Areacircle= π·r2=227×72=22×7=154 cm2

 

Example 2: What is the area of a circle with a diameter of 2 m? (Use π=3.14)

Solution: Areacircle=π4·d2=3.144×22=3.14 m2

 

Example 3: Find the circumference of a circle with a radius of 312 in.

Solution: C=2πr=2×227×312=2×227×72=22 in

Cheat Sheet

  • Relation between the diameter & radius of a circle: d=2r
  • Circumference of a circle: C=2πr
  • Area of a circle when the radius is known: Areacircle=π·r2
  • Area of a circle when the diameter is known: Areacircle=π4·d2

Blunder Areas

  • The radius is half of the diameter, not the vice-versa.
  • The area of a semi-circle is half the area of a circle.
  • The perimeter of a semi-circle is not half the perimeter of a circle.