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प्रश्न
Read the following passage:
Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking. After survey, it was decided to build rectangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and breadth of the rectangular playground are 14 units and 7 units, respectively. There are two quadrants of radius 2 units on one side for special seats. |
Based on the above information, answer the following questions:
- What is the total perimeter of the parking area?
- (a) What is the total area of parking and the two quadrants?
OR
(b) What is the ratio of area of playground to the area of parking area? - Find the cost of fencing the playground and parking area at the rate of ₹ 2 per unit.
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उत्तर
i. Given, Length of rectangular playground = 14 units
Breadth of rectangular playground = 7 units
Total perimeter of parking area = Perimeter of semi-circle + Breadth of rectangle
= πR + 7 ...`(("Diameter of semi-circle" = 7),("R" = 7/2))`
= `π xx 7/2 + 7`
= `22/7 xx 7/2 + 7`
= 11 + 7
= 18 units
ii. (a) Given, radius of the quadrant = 2 units
Area of two quadrants = `2 xx ((π"r"^2)/4)`
= `2 xx (π(2)^2)/4`
= 2π sq. units
Area of parking area = `(π"R"^2)/2`
= `π/2 xx (7/2)^2` ...`(∵ "Radius (R) of semicircle" = 7/2)`
= `22/7 xx 7/2 xx 7/2 xx 1/2`
= `77/4`
= 19.25
Total area of parking and two quadrants
= `2 xx 22/7 + 19.25`
= 6.28 + 19.25
= 25.53 sq. units
OR
(b) Required Ratio = `"Area of playground"/"Area of parking area"`
= `(7 xx 14)/(77/4)`
= `(14 xx 4)/11`
= `56/11`
iii. Perimeter of rectangle part = 2 (Length + Breadth)
= 2 (7 + 14)
= 2 × 21
= 42 units
Perimeter of parking area = πR
= `π xx 7/2`
= `7/2 xx 22/7`
= 11 units
∴ Perimeter of entire region = Perimeter of rectangular part + Perimeter of parking area
= 42 + 11 = 53 units
∴ Cost of fencing = ₹ 2 per unit
∴ Total cost = 53 × 2 = ₹ 106
