1 of 4

AREAS RELATED

TO CIRCLE

  • Sum based on Area of circle (part-II)

2 of 4

∴

r3 =

31.5 cm

A (Blue ring) =

=

=

Radius of blue circular region (r3) =

r2 + 10.5

π

(r32 –

r22)

22

7

×

(31.52

–

212)

22

7

×

(31.5

+

21)

(31.5

–

21)

=

∴

Area of blue ring is 1732.5 cm2

22

7

×

52.5

×

10.5

1.5

  1. The following figure depicts an archery target marked with its

five scoring areas from the centre outwards as Gold, Red, Blue,

Black and White. The diameter of the region representing Gold

score is 21 cm and each of the other bands is 10.5 cm wide.

Find the area of each of the five scoring regions.

Sol.

White

Black

Blue

Red

Gold

21 cm

10.5

10.5

10.5

10.5

Let us find area of Blue ring

Blue

Red

10.5

10.5

Gold

10.5

Let us find radius of blue circular region

A (Blue ring) =

A (Blue circular region) –

A (Red circular region)

πr32

– πr22

=

r2 = 21

= 1732.5

3 of 4

=

31.5 + 10.5

∴

42 cm

r4 =

∴

A (Black ring) =

=

=

=

∴

Area of black ring is 2425.5 cm2

= 2425.5 cm2

Radius of black circular region (r4) =

r3 + 10.5

π(r42

– r32)

22

7

×

(422

–

31.52)

22

7

×

(42

+

31.5)

(42

–

31.5)

22

7

×

73.5

×

10.5

1.5

  1. The following figure depicts an archery target marked with its

five scoring areas from the centre outwards as Gold, Red, Blue,

Black and White. The diameter of the region representing Gold

score is 21 cm and each of the other bands is 10.5 cm wide.

Find the area of each of the five scoring regions.

Sol.

White

10.5

Let us find area of Black ring

Black

Blue

Red

Gold

10.5

10.5

10.5

10.5

Let us find radius of black circular region

A (Black ring) =

A (Black circular region) –

A (Blue circular region)

πr42

– πr32

=

r3 = 31.5

4 of 4

∴

52.5 cm

=

42 + 10.5

∴

A (White ring) =

=

=

=

∴

Area of white ring is 3118.5 cm2

= 3118.5 cm2

r5 =

Radius of white circular region (r5) =

r4 + 10.5

π

(r52 –

r42)

22

7

×

(52.52

–

422)

22

7

×

(52.5

+

42)

(52.5

–

42)

22

7

×

94.5

×

10.5

1.5

  1. The following figure depicts an archery target marked with its

five scoring areas from the centre outwards as Gold, Red, Blue,

Black and White. The diameter of the region representing Gold

score is 21 cm and each of the other bands is 10.5 cm wide.

Find the area of each of the five scoring regions.

Sol.

White

10.5

Black

Blue

Red

Gold

10.5

10.5

10.5

10.5

Let us find area of White ring

Let us find radius of White circular region

A (White ring) =

A (White circular region) –

A (Black circular region)

πr52

– πr42

=

r4 = 42