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# In the figure above, ABCD is a rectangle and the curved path is made

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Joined: 02 Sep 2009
Posts: 50042
In the figure above, ABCD is a rectangle and the curved path is made  [#permalink]

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29 Nov 2017, 22:52
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Difficulty:

45% (medium)

Question Stats:

58% (01:39) correct 42% (02:02) wrong based on 38 sessions

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In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24
(B) 32
(C) 48
(D) 64
(E) 192

Attachment:

2017-11-30_0948.png [ 45.01 KiB | Viewed 731 times ]

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Re: In the figure above, ABCD is a rectangle and the curved path is made  [#permalink]

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30 Nov 2017, 00:01
Bunuel wrote:

In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24
(B) 32
(C) 48
(D) 64
(E) 192

Attachment:
2017-11-30_0948.png

16 semicircles are 8 circles => $$8 * 2 \pi * r = 32 \pi$$
$$r = 2 => D = 4$$

6D * 2D = area ABCD
$$24 * 8 = 192$$
E
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Re: In the figure above, ABCD is a rectangle and the curved path is made  [#permalink]

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30 Nov 2017, 11:57
Bunuel wrote:

In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24
(B) 32
(C) 48
(D) 64
(E) 192

Attachment:
2017-11-30_0948.png

Let us assume the diameter of the semi-circle to be D.

From the given information, we can write :

$$16 * π* \frac{D}{2} = 32 π$$

$$D = 4$$

Now from the diagram, notice the length of the rectangle $$= 6*D = 6*4 = 24$$

And the breadth of the rectangle $$= 2D = 2 * 4 = 8$$

Thus, the area of the rectangle $$= L *B = 24 * 8 = 192$$

The correct answer is Option E.
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In the figure above, ABCD is a rectangle and the curved path is made  [#permalink]

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02 Dec 2017, 14:40
There are 16 semi-circles along the perimeter of the rectangle.

This equals to 8 circles with total circumference of 32π

So, Circumference of each circle is 4π

This equals to diameter per circle of 4 units.

So, In the Rectangle, There are six diameters along the length equaling 24 units and two diameters along width equaling 8 units.

Therefore, Area of Rectangle is 24*8 = 192 sq. Units

Ans E

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Re: In the figure above, ABCD is a rectangle and the curved path is made  [#permalink]

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03 Dec 2017, 18:56
Bunuel wrote:

In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24
(B) 32
(C) 48
(D) 64
(E) 192

Attachment:
2017-11-30_0948.png

Since the curved path is made up of 16 semicircles, each semicircular arc is 32π/16 = 2π. Thus, the diameter of each semicircle is 4 (notice that ½ x 4π = 2π). Since the length of the rectangle is made up of 6 diameters, the length = 24, and, since the width is made up of 2 diameters, the width = 8, so the area is 24 x 8 = 192.

Answer: E
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Re: In the figure above, ABCD is a rectangle and the curved path is made &nbs [#permalink] 03 Dec 2017, 18:56
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# In the figure above, ABCD is a rectangle and the curved path is made

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