KnowledgeBoat Logo
|

Mathematics

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹50 per m2.

Mensuration

68 Likes

Answer

Let the radius of circular plot = R meters.

Given,

Circumference of circular plot = 44 m

2πR = 44

⇒2×227×R=44⇒R=44×72×22⇒R=7 m.\Rightarrow 2 \times \dfrac{22}{7} \times R = 44 \\[1em] \Rightarrow R = \dfrac{44 \times 7}{2 \times 22} \\[1em] \Rightarrow R = 7 \text{ m}.

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹50 per m^2. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

From figure,

Radius of outer circle = 7 + 3.5 = 10.5 m.

Area of road = Area of outer circle - Area of inner circle

= π(10.5)2 - π(7)2

= 110.25π - 49π

= 61.25π

= 227×61.25\dfrac{22}{7} \times 61.25

= 192.5 m2.

Cost of paving road = Area of road × Rate of paving the road

= 192.5 × 50

= ₹9625.

Hence, cost of paving the road = ₹9625.

Answered By

39 Likes

Related Questions