Fig. 12.3 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 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Fig. 12.3 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 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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Fig. 12.3 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 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Fig 12.3

Solution:

⇨ For Gold

⇨ d = 21 cm

⇨ r = 21/2 cm

⇨ Area Of Gold Region

$Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.$

$Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.$

$Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.$

$Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.$

$Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.$

⇨ For Red

⇨ r = 21/2 + 10.5 = 21 cm

⇨ Area Of Red Region

$\large =\pi r^{2}$

$\large =\frac{22}{7}\times \left ( 21^{2} \right )$

$\large =\frac{22}{7}\times 441$

$\large =\frac{9702}{7}$

$\large =1386 cm^2$

⇨ Area Of Red band = Area Of Red Region - Area Of Gold Region

⇨ Area Of Red band = 1386 - 346.5

⇨ Area Of Red band = 1039.5 $\large cm^2$

⇨ For Blue

⇨ r = 21 + 10.5 = 31.5 or 63/2 cm

⇨ Area Of Blue Region

$\large =\pi r^{2}$

$\large = \frac{22}{7}\times \left ( \frac{63}{2} \right )^{2}$

$\large = \frac{22}{7}\times \frac{3969}{4}$

$\large = \frac{87318}{28}$

$\large = 3118.5 cm^2$

⇨ Area Of Blue band = Area Of Blue Region - Area Of Red Region

⇨ Area Of Blue band = 3118.5 - 1386

⇨ Area Of Blue band = 1732.5 $\large cm^2$

⇨ For Black

⇨ r = 31.5 + 10.5 = 42 cm

⇨ Area Of Black Region

$\large =\pi r^{2}$

$\large = \frac{22}{7}\times \left ( 42\right )^{2}$

$\large = \frac{22}{7}\times 1764$

$\large = \frac{38808}{7}$

$\large = 5544 cm^2$

⇨ Area Of Black band = Area Of Black Region - Area Of Blue Region

⇨ Area Of Black band = 5544 - 3118.5

⇨ Area Of Black band = 2425.5 $\large cm^2$

⇨ For White

⇨ r = 42 + 10.5 = 52.5 or 105/2 cm

⇨ Area Of White Region

$\large =\pi r^{2}$

$\large = \frac{22}{7}\times \left ( \frac{105}{2} \right )^{2}$

$\large = \frac{22}{7}\times \frac{11025}{4}$

$\large = \frac{242550}{28}$

$\large = 8662.5 cm^2$

⇨ Area Of White band = Area Of White Region - Area Of Black Region

⇨ Area Of Black band = 8662.5 - 5544

⇨ Area Of Black band = 3118.5 $\large cm^2$

Exercise 12.1

1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

2. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

3. Fig. 12.3 depicts an archery target marked with its five scoring regions from the center 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.

4. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

5. Tick the correct answer in the following and justify your choice : If the perimeter and thearea of a circle are numerically equal, then the radius of the circle is