An archery target marked with its five scoring regions 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.
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Verified answer
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:
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
Step-by-step explanation:
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