Question

Fig. 12.3 depicts an archery target marked with its five
wing regions from the centre outwards as Gold, Red, Blue.
Had and White. The diameter of the region representing
Geld score is 21 cm and each of the other hands is 10.5 cm
Find the area of each of the five scoring regions.​

Answer 1

Step-by-step explanation:

SOLUTION:

GIVEN:

Diameter of Gold region= 21 cm

Radius of gold region= 21/2= 10.5 cm

Area of Gold Region = πr²

= π(10.5)² =( 22/7)× 110.25 = 346.5 cm²

Area of Gold Region= 345.5 cm²

Radius of red region = Radius for gold + red region= 10.5 + 10.5= 21 cm

Area of Red Region = π²(21² - 10.5²)

[Area of a ring= π (R²-r²), where R= radius of outer ring & r= radius of inner ring]

= 22/7 (21² – 10.5²) [ a²-b²= (a+b)(a-b)]

= 22/7 (21 + 10.5)(21 – 10.5)

= (22/7 )x 31.5 x 10.5 = 1039.5 cm²

Area of Red Region = 1039.5 cm²

Radius of blue region = Radius of blue region = Now radius for gold + red+ blue region= 21+10.5= 31.5 cm

Area of Blue Region = π(31.5² – 21²)

= 22/7 (31.5² - 21²)

= 22/7 (31.5 +21)(31.5 - 21)

= (22/7 )x 52.5 x 10.5 = 1732.5 cm²

Area of Blue Region =1732.5 cm²

Now,

Radius of black region= radius for gold + red+ blue + black region= 31.5+10.5= 42 cm

Area of Black Region = π(42² – 31.5²)

= 22/7 (42²-31.5² )

= 22/7 (42+31.5)(42-31.5)

= (22/7 )x 73.5 x 10.5 = 2425.5 cm²

Area of Black Region =2425.5 cm²

Now

Radius of white region= radius for gold + red+ blue + black+ white region= 42+10.5= 52.5 cm

Area of White Region= π(52.5² – 42²)

= 22/7 (52.5²-42² )

= 22/7 (52.5+42)(52.5-42)

= (22/7 )x 94.5 x 10.5 = 3118.5 cm²

Area of white Region =3118.5 cm²

Answer 2

$\huge\color{red}{\underline{\underline {Given}}}$

ᴅɪᴀᴍᴇᴛᴇʀ ᴏꜰ ɢᴏʟᴅ ʀᴇɢɪᴏɴ= 21 ᴄᴍ

ᴛʜᴇɴ, ʀᴀᴅɪᴜꜱ ᴏꜰ ɢᴏʟᴅ ʀᴇɢɪᴏɴ =21/2 = 10.5 ᴄᴍ

$\huge\color{red}{\underline{\underline {To \: Find}}}$

The area of each of the five scoring regions.

$\huge\color{red}{\underline{\underline {Solution}}}$

ᴀʀᴇᴀ ᴏꜰ ɢᴏʟᴅ ʀᴇɢɪᴏɴ

= πʀ^2 = 22/7 (10.5)^2

= 22/7 x 110.25

= 346.5 ᴄᴍ ꜱq.

ʀᴀᴅɪᴜꜱ ꜰᴏʀ ɢᴏʟᴅ + ʀᴇᴅ ʀᴇɢɪᴏɴ

= 10.5 + 10.5

= 21 ᴄᴍ [ ʙʏ ɢɪᴠᴇɴ ᴄᴏɴᴅɪᴛɪᴏɴ ]

•°• ᴀʀᴇᴀ ꜰᴏʀ ʀᴇᴅ ʀᴇɢɪᴏɴ

= 22/7 [(21)^2 - (10.5)^2]

[ °•° ᴀʀᴇᴀ ᴏꜰ ᴀ ʀɪɴɢ = π (ʀ^2 - ʀ^2)

ᴡʜᴇʀᴇ, ʀ = ʀᴀᴅɪᴜꜱ ᴏꜰ ᴏᴜᴛᴇʀ ʀɪɴɢ, ᴀɴᴅ

ʀ = ʀᴀᴅɪᴜꜱ ᴏꜰ ɪɴɴᴇʀ ʀɪɴɢ.]

= 22/7 (21)^2 - 22/7 (10.5)^2

= 1386 - 346.5

= 1039.5 ᴄᴍ ꜱq.

ɴᴏᴡ, ʀᴀᴅɪᴜꜱ ꜰᴏʀ ɢᴏʟᴅ + ʀᴇᴅ + ʙʟᴜᴇ ʀᴇɢɪᴏɴ = 21 + 10.5 = 31.5 ᴄᴍ [ ʙʏ ɢɪᴠᴇɴ ᴄᴏɴᴅɪᴛɪᴏɴ ]

•°• ᴀʀᴇᴀ ꜰᴏʀ ʙʟᴜᴇ ʀᴇɢɪᴏɴ

= 22/7 [(31.5)^2 - (21)^2]

= 22/7 ( 31.5)^2 - 22/7(21)^2

= 3118.5 - 1386

= 1732.5 ᴄᴍ ꜱq.

ɴᴏᴡ, ʀᴀᴅɪᴜꜱ ꜰᴏʀ ɢᴏʟᴅ + ʀᴇᴅ + ʙʟᴜᴇ + ʙʟᴀᴄᴋ ʀᴇɢɪᴏɴ

= 31.5 + 10.5

= 42 ᴄᴍ [ ʙʏ ɢɪᴠᴇɴ ᴄᴏɴᴅɪᴛɪᴏɴ ]

•°• ᴀʀᴇᴀ ꜰᴏʀ ʙʟᴀᴄᴋ ʀᴇɢɪᴏɴ

= 22/7 [(42)^2 - (31.5)^2]

= 22/7 (42)^2 - 22/7 (31.5)^2

= 5544 - 3118.5

= 2425.5 ᴄᴍ ꜱq.

ʀᴀᴅɪᴜꜱ ꜰᴏʀ ɢᴏʟᴅ + ʀᴇᴅ + ʙʟᴜᴇ + ʙʟᴀᴄᴋ + ᴡʜɪᴛᴇ ʀᴇɢɪᴏɴ

= 42 + 10.5

= 52.5 ᴄᴍ [ ʙʏ ɢɪᴠᴇɴ ᴄᴏɴᴅɪᴛɪᴏɴ ]

•°• ᴀʀᴇᴀ ꜰᴏʀ ᴡʜɪᴛᴇ ʀᴇɢɪᴏɴ

= 22/7 [(52.5)^2 - (42)^2]

= 22/7 (52.5)^2 - 22/7 (42)^2

= 8662.5 - 5544

= 3118.5 ᴄᴍ ꜱq.

$\huge\color{red}{\underline{\underline {Direct \:Answer}}}$

GOLD - 346.5 cm sq.

RED - 1039.5 cm sq.

BLUE - 1732.5 cm sq.

BLACK - 2425.5 cm sq.

WHITE - 3118.5 cm sq.