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605-655 (Medium)|   Geometry|      
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Bunuel
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In the figure above, ABCD is a rectangle and the curved path is made 29 Nov 2017, 22:52
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45% (medium)

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65% (01:59) correct 35% (01:43) wrong based on 89 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

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E
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In the figure above, ABCD is a rectangle and the curved path is made 30 Nov 2017, 00:01
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Bunuel

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

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2017-11-30_0948.png
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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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In the figure above, ABCD is a rectangle and the curved path is made 30 Nov 2017, 11:57
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Bunuel

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

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2017-11-30_0948.png
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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 02 Dec 2017, 14:40
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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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In the figure above, ABCD is a rectangle and the curved path is made 03 Dec 2017, 18:56
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Bunuel

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

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2017-11-30_0948.png
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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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In the figure above, ABCD is a rectangle and the curved path is made 15 Feb 2021, 09:30
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We can see that each side is split up into discrete regions.

L = 6 pieces
W = 2 pieces

(6 x 2) + (2 x 2) = 16 pieces

32π / 16 = 2π <--- Perimeter of semi-circle

2π x 2 = 4π <--- Perimeter of full circle

4π = 2πr <--- Circumference

r = 2 <--- Radius

d = 2 x 2 <--- Diameter

4 x 6 = 24 <--- Length of rectangle

4 x 2 = 8 <--- Width of rectangle

A = 24 x 8 = 192 <--- Area of rectangle

E is the answer.
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