5. Hit the target (Bullseye)
Can you hit the bullseye? Bullseye or Archery
is the sport of hunting or shooting at targets
using a bow and arrows. Archery target is
formed with concentric circles. Look at the figure
shown here.
The figure depicts an archery target marked
with its five scoring areas form the centre outwards
as Gold, Red, Blue, Black and White. The diameter of the region representing gold
scores is 21cm and each of the other bands is 10.5cm wide.
(a) The area of the region representing Gold scoring area is
(i) 346.5 cm2 (ii) 372 cm2 (iii) 368.85cm2 (iv) 390cm2
(b) Radius of the region representing Gold and Red scoring area is
(i) 42 cm (ii) 52.5cm (iii) 21cm (iv) 44cm
(c) The diameter of the archery target is
(i) 90cm (ii) 100 cm (iii) 105 cm (iv) 110cm
(d) The area of the region representing red scoring area is
(i) 572.8 cm2 (ii) 1039.5 cm2 (iii) 940.8 cm2 (iv) 1260 cm2
(e) Radius of region representing Gold, Red, Blue and Black scoring area is
(i) 10.5 cm (ii) 21 cm (iii) 42 cm (iv) 84 cm
Answers
Given : Hit the target (Bullseye)
five scoring areas form the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing gold scores is 21cm and each of the other bands is 10.5cm wide.
To Find : (a) The area of the region representing Gold scoring area is
(i) 346.5 cm2 (ii) 372 cm2 (iii) 368.85cm2 (iv) 390cm2
(b) Radius of the region representing Gold and Red scoring area is
(i) 42 cm (ii) 52.5cm (iii) 21cm (iv) 44cm
(c) The diameter of the archery target is
(i) 90cm (ii) 100 cm (iii) 105 cm (iv) 110cm
(d) The area of the region representing red scoring area is
(i) 572.8 cm2 (ii) 1039.5 cm2 (iii) 940.8 cm2 (iv) 1260 cm2
(e) Radius of region representing Gold, Red, Blue and Black scoring area is
(i) 10.5 cm (ii) 21 cm (iii) 42 cm (iv) 84 cm
Solution:
Gold, Red, Blue, Black and White
Diamter of Gold = 21 cm => Radius = 10.5 cm Area = πr² = (22/7)(10.5)² = 346.5 cm²
The area of the region representing Gold scoring area is 346.5 cm²
Diamter of Red = 21 +10.5 + 10.5 cm = 42 cm => Radius =21 cm
Radius of the region representing Gold and Red scoring area is 21 cm
Area = πr² = (22/7)(21)² = 1386 cm²
The area of the region representing Red scoring area = 1386 - 346.5 = 1,039.5 cm²
Radius of region representing Gold, Red, Blue and Black scoring area is
= ( 21 + 21 + 21 + 21 )/2 = 42 cm
The diameter of the archery target is 21 + 21 + 21 + 21 + 21 = 105 cm
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Step-by-step explanation:
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