The radius of the inner circle r = 21m
The path is around the inner circle.
Therefore, the radius of the outer circle, R = 21 + 14 = 35 m
The area of the circular path = π(R² − r² ) sq.units
= \(\frac { 22 }{ 7 } \)x(35² - 21²)
= \(\frac { 22 }{ 7 } \) x (35 x 35) - (21 x 21)
= \(\frac { 22 }{ 7 } \) x (1225 - 441)
= \(\frac { 22 }{ 7 } \) x 784
= 22 x 112 = 2464 m²

The radius of the outer circle, R = 10 m
The radius of the inner circle, r = 3 m
The area of the circular path =Area of outer circle −Area of inner circle
= πR² − πr²
= π(R² − r² ) sq.units
= \(\frac { 22 }{ 7 } \) x (10² - 3²)
= \(\frac { 22 }{ 7 } \) x (10 x 10)-(3 x 3))
= \(\frac { 22 }{ 7 } \)x (100 - 9)
= \(\frac { 22 }{ 7 } \) x 91
= 286 m²

To find the perimeter of the quadrant disc, we need to find the circumference of quadrant shape.
Given that radius (r) = 14 cm.
We know that the circumference of circle = 2πr units.
So, the circumference of the quadrant arc = \(\frac { 1 }{ 4 } \) x 2πr
 =\(\frac { \pi r }{ 2 } \)
 =\(\frac { 22 }{ 7 } \times \frac { 14 }{ 2 } \)
 = 22 cm
Given, the radius of the circle = 14 cm
Thus, perimeter of required quadrant shaped disc = 14 +14 + 22
 = 50 cm.

In this shape, we have to calculate the circumference of semicircle on each side of the rectangle. The outer boundary of this figure is made up of semicircles of two different sizes. Diameters of each of the semicircles are 7 cm and 14 cm. We know that the circumference of the circle = πd units.
Circumference of the semicircular part = \(\frac { 1 }{ 2 } \)πd units
Hence, the circumference of the semicircle having diameter 7 cm is,
= \(\frac { 1 }{ 2 } \) x \(\frac { 22 }{ 7 } \) x 7 = 11 cm
Circumference of the pair of semicircular parts (II and IV) = 2 x 11 = 22 cm
Similarly, circumference of the semicircle having diameter 14 cm is,
= \(\frac { 1 }{ 2 } \) x \(\frac { 22 }{ 7 } \) x 14 = 22 cm
Circumference of the pair of semicircular parts (I and III) = 2 x 22 = 44 cm.
Perimeter of the given shape = 22 + 44 = 66 cm.

The radius of the poultry farm is = 420 m
The length of the barbed wire for fencing the poultry farm is equal to the circumference of the circle.
We know that the circumference of the circle = 2πr units
= 2 x \(\frac { 22 }{ 7 } \) x 420
= 2 x 22 x 60
The length of the barbed wire to fence the poultry farm = 2640 m
The cost of fencing the poultry farm at the rate of Rs.12 per metre = 2640 x 12
= Rs.31,680
Given that he has Rs.30,000 with him.
The excess amount required = Rs.31,680 − Rs.30,000 = Rs.1,680.