Question

Given 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.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

[FIGURE IS IN THE ATTACHMENT]

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 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


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 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 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

HOPE THIS WILL HELP YOU....

Answer 2

ANSWER
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Diameter of gold circle = 21 cm So, Radius of gold =


/2 = 21/2 cm = 10.5 cm Now, Area of gold =


rGOLD2 = 22/7 × 10.5 × 10.5 = 346.5 cm2


Now , Radius of red = Radius of gold + width of


band = 10.5 + 10.5 = 21 cm Area of (red + gold )


= 22/7×21×21 = 1386 cm2 Area


of red = Area of (Red + gold ) – area of gold = 1386 – 346.5 = 1039.5 Radius of blue = radius


of red + width of band = 21 + 10.5 = 31.5 cm


Area of (Gold + red + blue) = πr2 = 22/7×(31.5)2 = 22/7×31.5×31.5 = 22 × 4.5 ×31.5 = 3118.5 cm2



Area of blue = Area of (red + gold + blue) – Area of (red + gold) = 3118.5 – 1386 = 1732.5 cm2 Radius of black = radius of blue + width of band = 31.5 + 10.5 = 42 cm Area of (Gold + red + blue + black) = πr2 = 22/7 × (42




)2 = 22/7 × 42 × 42 = 5544 Area of black portion = (Area of red + gold + blue + black) –


(Area of red + gold + blue) = 5544 – 3118 . 5 = 2425.5 cm2 Radius of white = radius of black +





width of band = 42 + 10.5 = 52.5 cm Area of (Gold + red + blue + black + white) = πr2 = 22/7 × (52.5)2 = 22/7 × 52.5 × 52.5 = 8662.5 Area of white portion = (Area of gold + red + blue +



black + white ) – (Area of red + gold + blue + black) = 8662.5 – 5544 = 3118 .5 cm2



3118. 5 CM IS THE ANSWER