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Retired Moderator V
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The figure above represents a rectangular parking lot that is 30 meter  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 63% (01:31) correct 37% (01:14) wrong based on 125 sessions

HideShow timer Statistics The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?

(A) $$1,350π$$
(B) $$1,200 + 400π$$
(C) $$1,200 + 300π$$
(D) $$1,200 + 200π$$
(E) $$1,200 + 150π$$

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Attachment: driveway.JPG [ 17.53 KiB | Viewed 1071 times ]

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Re: The figure above represents a rectangular parking lot that is 30 meter  [#permalink]

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HKD1710 wrote: The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?

(A) $$1,350π$$
(B) $$1,200 + 400π$$
(C) $$1,200 + 300π$$
(D) $$1,200 + 200π$$
(E) $$1,200 + 150π$$

Please refer the enclosed diagram,

Area of the lot and driveway(EXCLUDING the shaded region)=Total area of the lot and driveway- Area of the shaded region(or shaded semicircle)
=(Area of the rectangle of size 30x40 +Area of the bigger semicircle with radius 20m)- Area of the shaded semi-circle with radius 10m
$$=30*40+\frac{1}{2}*\pi*20^2-\frac{1}{2}*\pi*10^2$$
=$$1200+\frac{1}{2}*\pi*(20^2-10^2)$$
=$$1200 + 150π$$ sq. meter
Attachments driveway.JPG [ 33.82 KiB | Viewed 944 times ]

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Re: The figure above represents a rectangular parking lot that is 30 meter  [#permalink]

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Area of rectangle 40*30 = 1200

Area of smal semi circle = piR^2 / 2 = 10^2 / 2 = 50

Area of large semi circle = piR^2/2 = 20^2 / 2 = 200

Area of large semicircle - area of small semicircle = 200 -50 = 150

Area of the lot and driveway 1200+150p

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Re: The figure above represents a rectangular parking lot that is 30 meter  [#permalink]

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HKD1710 wrote: The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?

(A) $$1,350π$$
(B) $$1,200 + 400π$$
(C) $$1,200 + 300π$$
(D) $$1,200 + 200π$$
(E) $$1,200 + 150π$$

Project PS Butler : Question #86

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Attachment:
driveway.JPG

We can calculate the area by

Area of driveway = 1200

Area of not shaded semicircle = 200π

Area of shaded semicircle = 50π

Total area = 1200 +π (200 -50)
$$1,200 + 150π$$
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: The figure above represents a rectangular parking lot that is 30 meter   [#permalink] 12 Feb 2019, 08:12
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