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area of ​​circle

1-circle-

The length of the curved boundary of a circle is its perimeter, but the perimeter of the circle is called the circumference.

The circumference of a circle has a constant ratio with its diameter, which we denote by a Greek letter (pi).
* circumference/diameter =
* circumference = diameter x
either
* Perimeter = 2r x (r is the radius of the circle)
either
* circumference = 2πr
is an irrational number whose decimal expansion is a non-terminating frequency (non-terminating non recurring). Still we keep the value of as 22/7 or 3.14 to solve the problems.
sector (sector) – The region in the interior of the circle which is bounded by two radii and corresponding arc is the sector of the circle.

area of ​​circle

segment (segment of circle) – The region in the interior of the circle which is bounded by the chord and the corresponding arc (arc) of the circle is the segment of the circle.
Sector with less area minor sector to the sector with more area Major sector it is said. Similarly there are minor segments and major segments.
If the angle subtended by the chords in a sector at the center of the circle is n°, then –
Area of ​​sector= n/360 x r2
If the angle subtended by the chords in a sector at the center of the circle is n°, then –

2-Important Question-

Question 1: The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle whose circumference is equal to the sum of the circumferences of these two circles.

Answer: circumference of the first circle

=2πr=2π×19=38π cm=2πr=2π×19=38π cm

Circumference of second circle =18π cm=18π cm

or, 2πr=56π2πr=56π

or, 2r=562r=56

or, r=28 cmr=28 cm

According to the question, the circumference of the largest circle

=38π+18π=56π cm=38π+18π=56π cm


Question 2: The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle whose area is equal to the areas of these two circles.

Answer: Area of ​​the first circle =πr2=πr2

=π82=64π sq cm=π82=64π sq cm

Area of ​​the second circle =π62=36π sq cm=π62=36π sq cm

According to the question, the area of ​​the largest circle =64π+36π=64π+36π

=100π sq cm=100π sq cm

or, r2=100ππr2=100π

or, r2=100r2=100

or, r=10 cmr=10 cm

Question 3: The given figure shows an archery target with five areas from the center outwards marked GOLD, RED, BLUE, BLACK and WHITE, from which points can be earned. The diameter of the field containing the GOLD number is 21 cm and each other strip is 10.5 cm wide. Find the area of ​​each of these five fields which fetch the marks.

Answer: Area of ​​Gold Digit =πr2=πr2

=π10.52=110.252=346.5 sq cm=π10.52=110.252=346.5 sq cm

Area of ​​Red Point =πr2=πr2

=π212−π10.52=π212-π10.52

=π(212–10.52)=π(212–10.52)

=π(21+10.5)(21–10.5)=π(21+10.5)(21–10.5)

=π×31.5×10.5=1039.5 sq cm=π×31.5×10.5=1039.5 sq cm

Area of ​​Blue Point =πr2=πr2

=π(31.52–212)=1732.5 sq cm=π(31.52–212)=1732.5 sq cm

Area of ​​Black number =πr2=πr2

=π(422–31.52)=2425.5 sq cm=π(422–31.52)=2425.5 sq cm

Area of ​​White Point =πr2=πr2

=π(52.52–422)=3118.5 sq cm=π(52.52–422)=3118.5 sq cm

Question 4: The diameter of each wheel of a car is 80 cm. If the car is traveling at 66 kmph, how many revolutions does each wheel make in 10 minutes?

Answer: Distance covered in 10 minutes =6660×10=11 km=6660×10=11 km

Perimeter =πd=80π=πd=80π

=227×80 cm=227×80 cm

=227×80×11000×100 km=227×80×11000×100 km

number of rounds

=11×1000×100×722×80=11×1000×100×722×80

=4375=4375

Question 5: If the perimeter and area of ​​a circle are numerically equal, then the radius of that circle is:

  1. 2 units
  2. unit
  3. 4 units
  4. 7 units

Answer: (A) 2 units

Explanation:

2πr=πr22πr=πr2
or, r2πr=2πr2πr=2

or, r=2

Read in Hindi: area of ​​circle
in Hindi

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