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Math Expert
Joined: 02 Sep 2009
Posts: 47001

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28 Nov 2017, 21:12
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92% (00:43) correct 8% (00:00) wrong based on 12 sessions

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The design indicated above was made from a circular piece of cardboard by dividing it into sections of equal size and then shading every other section. If the design has a diameter of 30 centimeters, the area of the shaded portion shown is how many square centimeters?

(A) 37.5π
(B) 112.5π
(C) 225π
(D) 450π
(E) 900π

Attachment:

2017-11-29_0805_002.png [ 27.71 KiB | Viewed 410 times ]

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28 Nov 2017, 23:40
d= 30 $$cm^2$$
r= 15 $$cm^2$$
let a be the area of one piece of the shaded design. Since the sections are of equal size, 12 a= area of the circle
We need to find 6a
2(6a) = π $$15^2$$
6a = 112.5π $$cm^2$$

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01 Dec 2017, 07:51
Bunuel wrote:

The design indicated above was made from a circular piece of cardboard by dividing it into sections of equal size and then shading every other section. If the design has a diameter of 30 centimeters, the area of the shaded portion shown is how many square centimeters?

(A) 37.5π
(B) 112.5π
(C) 225π
(D) 450π
(E) 900π

Attachment:
2017-11-29_0805_002.png

We see the circle is broken up into 12 equal parts; 6 are shaded and 6 are not. Thus, the shaded region is 1/2 the area of the entire circle.

Since the area of the entire circle is 15^2 x π = 225π, the area of shaded region is:

1/12 x 225π = 112.5π

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