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Sub 505 (Easy)|   Geometry|      
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Bunuel
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Two circles are inscribed in a rectangle as shown above. What is the 15 Jun 2020, 07:48
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Two circles are inscribed in a rectangle as shown above. What is the area of the shaded region?


A. \(200 - 25\pi\)

B. \(200 - 50\pi\)

C. \(100 - 20\pi\)

D. \(100 - 25\pi\)

E. \(100 - 30\pi\)



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D
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Two circles are inscribed in a rectangle as shown above. What is the 15 Jun 2020, 07:57
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Bunuel

Two circles are inscribed in a rectangle as shown above. What is the area of the shaded region?


A. \(200 - 25\pi\)

B. \(200 - 50\pi\)

C. \(100 - 20\pi\)

D. \(100 - 25\pi\)

E. \(100 - 30\pi\)



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Area of rectangle = 20*10=200
Area of circle = \(\pi*r^2=\pi*5^2=25\pi\), so area of both circles = \(2*25\pi=50\pi\)

So area inside rectangle but outside the circle = \(200-50\pi\)

Area of the shaded portion = \(\frac{200-50\pi}{2}=100-25\pi\)

D
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Two circles are inscribed in a rectangle as shown above. What is the 15 Jun 2020, 08:04
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Bunuel

Two circles are inscribed in a rectangle as shown above. What is the area of the shaded region?


A. \(200 - 25\pi\)

B. \(200 - 50\pi\)

C. \(100 - 20\pi\)

D. \(100 - 25\pi\)

E. \(100 - 30\pi\)



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File comment: As per the circles are concerned,

In the illustration pic the shaded parts are symmetrical.

IMO ans is D
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Two circles are inscribed in a rectangle as shown above. What is the 15 Jun 2020, 08:07
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Bunuel

Two circles are inscribed in a rectangle as shown above. What is the area of the shaded region?


A. \(200 - 25\pi\)

B. \(200 - 50\pi\)

C. \(100 - 20\pi\)

D. \(100 - 25\pi\)

E. \(100 - 30\pi\)



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Area of shaded portion= area of triangle -area of a circle

= half x 20x10- pi x square of 5= 100- 25pi
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Two circles are inscribed in a rectangle as shown above. What is the 15 Jun 2020, 16:33
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Area of shaded region =
Area of one triangle = 1/2*10*20 = 100
Area of circle = pi\(5^2\) = 25pi
Therefore, 100 - 25pi
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Two circles are inscribed in a rectangle as shown above. What is the 15 Jun 2020, 18:41
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Is this a 700-level problem?

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inesricardette
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Two circles are inscribed in a rectangle as shown above. What is the 16 Jun 2020, 04:02
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First let’s calculate the area of the rectangle:
10x20= 200

Then we can calculate the area of both circles:
The diameter of both circles = 20
So each circle has a radius of 5
Area of each circle= 25pi

If you look at the figure, you can see that the shaded area is present twice in the rectangle so by removing both circle areas from the rectangle and dividing it by 2 we can find the shaded area:

(200 - 50 pi)/ 2 = 100- 25pi

AnswerD
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Two circles are inscribed in a rectangle as shown above. What is the 16 Jun 2020, 06:37
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As diagonal of the rectangle cuts the same in half. It is safe to assume that it will also cut the 2 inscribed (similar) circles in same proportion.

SO effectively
Area of shaded region = Area of traingle - are of circle
10*20/2 - Pie*(10/2)^2
100- 25Pie

IMO D
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