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The figure above represents a rectangular parking lot that is 30 meter

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

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New post 18 Dec 2018, 10:27
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  45% (medium)

Question Stats:

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

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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
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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New post 18 Dec 2018, 21:13
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HKD1710 wrote:
Image

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
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driveway.JPG
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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New post 19 Dec 2018, 12:14
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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New post 12 Feb 2019, 08:12
HKD1710 wrote:
Image

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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Re: The figure above represents a rectangular parking lot that is 30 meter   [#permalink] 12 Feb 2019, 08:12
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