Question

The inner circumference of a circular track is 440 cm. The track is 14 cm
wide. Find the cost of levelling it at 20 paise/sqm. Also find the cost of
putting up a fence along outer circle at Rs. 2 per metre.

Answer 1

The inner circumference = 440 cm
CIRCUMFERENCE = 2 × 22/7 × r

440 = 44/7 × r
=> r = 440 × 7/44
r = 70 cm

Diameter of inner circle = 2 × r
= 140 cm

On both sides the of the inner diameter the circular track is 14 cm wide 

Therefore,

Outer diameter = Inner diameter + 14 + 14

=> 140 + 14 + 14
=> 158 cm

OUTER DIAMETER = 158 cm

Answer 2

Inner circumference = 2π1 = 440m

Inner radius, r1 = $\sf{\frac{440×7}{2×22}=70m}$

Outer radius,r2 = 70 + 14 = 84m

Area of the track =

= $\sf{\pi( {r2}^{2} - {r1}^{2} )}$

= $\sf{ \frac{22}{7} (( {84)}^{2} - ( {70)}^{2} ) {m}^{2}}$

= $\sf{\frac{22}{7} \times (84 + 70)(84 - 70) {m}^{2}}$

= $\sf{ \frac{22}{7} \times 154 \times 14 {m}^{2}}$

= $\sf{6776 {m}^{2}}$

Cost of levelling the track at the rate of Rs. 0.50 per $\sf{{m}^{2}}$

= $\sf{Rs.6776×0.50}$

= $\sf{Rs.3388}$

Outer circumference

= $\sf{2πr2 = 2 \times \frac{22}{7} \times 84 }$

= $\sf{528m}$

Cost of putting up a fencing along the outer circle at the rate of Rs. 15 per metre

= $\sf{Rs.528×15}$

= $\sf{Rs.7920}$