Question

the daimeter of a circular park is 80 meters. a 4 m wide road runs outside ariund it. find the cost of constructing the road at ₹10 per sq metre.
​

Answer 1

• Inner Diameter of park = 80 m
• Inner Radius of the park = 40 m

.°. Outer Radius of the park = (40 + 4) = 44 m

Now,

${ \mathtt{Area \: \: of \: \: the \: \: path = \: \pi( {44}^{2} - {40}^{2} ) }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{22}{7} \times (1936 - 1600) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{22}{7} \times 336 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= 22 \times 48 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \mathbf{= 1056 \: {m}^{2} }}$

Hence,

Total cost for constructing the road = ₹(10 × 1056)

= ₹ 10560