Question

answer
depicts and archery target Marked with its 5 scoring region 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 band is 10.5 cm wide.find the area of each of the five scoring regions

Answer 1

Given , Diameter = 21cm.then the radius r1 will be 10.5 cm.

radius r2 = 10.5 + 10.5 = 21cm.

radius r3 = 21 + 10.5 = 31.5 cm.

radius r4 = 31.5 + 10.5 = 42 cm.

radius r5 = 42 + 10.5 = 52.5 cm.

Area of a gold region = pi r1^2 = 22/7 * (10.5)^2 = 346.5 cm^2.

Area of a red region = pi * r2^2 - 346.5 = 22/7 * (21)^2 - 346.5 = 1039.5 cm^2.

Area of a blue region = pi * r3^2 - 1386 = 1732.5 cm^2.

Area of a black region = pi * r4^2 - 1386 = 2425.5cm^2.

Area of a white region = pi * r5^2 - 5544 = 3118.5 cm^2.


Hope this helps!

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.