1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

There is a circular park near Ram’s house. In this park, there are rectangular and circular paths of width 1.5 m. The rectangular paths pass through center of the park. The local community decided to put grass beds on the entire pathway. The inner radius of the circular path is 8 m. If the distance between any of the gates and the circular path is 2.5 m, find the cost of laying grass beds on the entire pathway at 0.1 paise per square cm.(Consider overlapping areas as squares)

A

₹1550

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

₹1435

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

₹1431.75

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

₹1185

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C ₹1431.75 For circular path, the inner radius = 8 m So, the outer radius = (8 + 1.5) m = 9.5 m Area of the circular path = π [(outer radius)2−(inner radius)2] =π(9.52−82)=(3.14)×17.5m×1.5m=82.425m2 (Using identity a2−b2=(a+b)(a−b)) Radius of the park = Outer radius of circular path + Distance between the path and any gate = (9.5 + 2.5) m = 12 m Length of the rectangular pathways = Diameter of the park = 24 m So, area of 2 rectangular pathways = 2 × (lb) = 2 × 24 m × 1.5 m = 72 m2 Total area = (82.425 + 72) m2 = 154.425 m2 But we have taken 5 areas twice (shaded in the figure). These are the areas where rectangular paths are overlapping with the circular path. These overlapping areas are nearly square in shape. So, overlapping area = 5 × (1.5)2 = 5 × (2.25) = 11.25 m2 Hence, Total area = (154.425 – 11.25) m2 = 143.175 m2 Cost of laying grass beds = 0.1 paisa per cm2 ​ So, for 1 m2 i.e. 10000 cm2, cost = (0.1 × 10000) paise = 1000 paise = ₹10 Total cost = (₹ 10 / m2) × 143.175 m2 = ₹1431.75

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Later Mughals
HISTORY
Watch in App
Explore more
Join BYJU'S Learning Program