Q- Depicts 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 21cm and each of the other bands is 10.5cm wide. Find the area of the five scoring regions.
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Answers
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:
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