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555-605 (Medium)|   Geometry|      
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In the figure above, five semicircles are drawn on the number line. Wh 27 Nov 2017, 23:34
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In the figure above, five semicircles are drawn on the number line. What is the total shaded area?

(A) 5π/16
(B) 5π/8
(C) 5π/4
(D) 5π/2
(E) 5π


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B
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In the figure above, five semicircles are drawn on the number line. Wh 28 Nov 2017, 00:07
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B.
Area of one shaded region is (pi.1^2)/4*(1/2) =pi/8
For 5 such regions area =5.pi/8


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In the figure above, five semicircles are drawn on the number line. Wh 29 Nov 2017, 04:33
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Radius of first shaded region = 1/2.
=> Area of first shaded region= pi*1/2*1/2=pi/4.
=>Area of five identical regions= 5*pi/4=5pi/4.

IMO:c
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In the figure above, five semicircles are drawn on the number line. Wh 29 Nov 2017, 04:35
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Utkarsh KOhli
Radius of first shaded region = 1/2.
=> Area of first shaded region= pi*1/2*1/2=pi/4.
=>Area of five identical regions= 5*pi/4=5pi/4.

IMO:c
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You are calculating for the entire circle. However here it’s semicircle


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In the figure above, five semicircles are drawn on the number line. Wh 29 Nov 2017, 04:39
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Sasindran
Utkarsh KOhli
Radius of first shaded region = 1/2.
=> Area of first shaded region= pi*1/2*1/2=pi/4.
=>Area of five identical regions= 5*pi/4=5pi/4.

IMO:c

You are calculating for the entire circle. However here it’s semicircle


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Thank you for correcting me.
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In the figure above, five semicircles are drawn on the number line. Wh 29 Nov 2017, 18:18
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Bunuel

In the figure above, five semicircles are drawn on the number line. What is the total shaded area?

(A) 5π/16
(B) 5π/8
(C) 5π/4
(D) 5π/2
(E) 5π


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The area of each semicircle is 1/2 x (1/2)^2 x π = (1/8)π, so the area of the entire shaded region is 5 x (1/8)π = (5/8)π = 5π/8.

Answer: B
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In the figure above, five semicircles are drawn on the number line. Wh 23 Aug 2019, 03:27
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The area of a semicircle is given by \(\frac{π*r^2}{2}\), where r is the radius of the semi-circle.

From the diagram, we can understand that the diameter of each semi-circle is 1 unit. Therefore, the radius of each semicircle is ½ unit.

The area of one semicircle = ½ * π*\((\frac{1}{2})^2\) = \(\frac{π}{8}\).

There are 5 such semicircles, therefore, the total shaded area = \(\frac{5* π}{8}\).

The correct answer option is B.

Hope this helps!
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