a rectangular Garden is 14o M long and 70 wide in the middle of the ground there is a circle pond of radius 42 cm find the cost of turfing the remaining portion at rupees 6.50 per square metre
Answers
Area of garden =L*B
= 140*70=9800m sq
Area of pond =pi*r^2
22/7*42*42
22*6*42
5544m sq
Area of remaining part = 9800-5544
4256m sq
Cost=6.50*4256= Rs 27664
Solution :
The rectangular garden's
• length = 140 m
• width = 70 m
Thus, the area of the garden
= length × width
= 140 × 70 m²
= 9800 m²
The radius of the circular pond in the middle of the rectangular garden
= 42 cm
= 0.42 m
Thus, the area of the circular pond
= π × 0.42 m²
= (22 / 7) × 0.42 m²
= 1.32 m²
So, the area of the remaining portion (the area of the garden except the pond in the middle of it)
= (the area of the rectangular garden) - (the area of the circular pond)
= (9800 - 1.32) m²
= 9798.68 m²
Hence, the cost of turfing the remaining portion at Rs 6.50 per square meter
= Rs (6.50 × 9798.68)
= Rs 63691.42
••• In question, if the circular pond's radius be 42 m,
the area of the pond be
= π × 42² m²
= 1764π m²
= 1764 × 22 / 7 m²
= 5544 m²
So, the portion's area be
= (9800 - 5544) m²
= 4256 m²
Hence, the required cost of turfing the remaining portion is
= Rs (6.50 × 4256)
= Rs 27664