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# In the rectangular solid below, the three faces shown have areas 12, 1

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Math Expert
Joined: 02 Sep 2009
Posts: 55274
In the rectangular solid below, the three faces shown have areas 12, 1  [#permalink]

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07 Jul 2017, 00:44
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:13) correct 18% (00:57) wrong based on 48 sessions

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In the rectangular solid below, the three faces shown have areas 12, 15, and 20. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1800
(E) 3600

Attachment:

2017-07-07_1143.png [ 1.11 KiB | Viewed 764 times ]

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Re: In the rectangular solid below, the three faces shown have areas 12, 1  [#permalink]

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07 Jul 2017, 01:45
Since the areas of the three faces of the cuboid, are 12,15 and 20,
and each of the faces are rectangles, area is ab,bc and ac

For ab = 12, bc = 15 and ac = 20, the sides have to be a = 3,b = 4, and c = 5.
The volume of the cuboid is a*b*c = 3*4*5 = 60(Option A)
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Re: In the rectangular solid below, the three faces shown have areas 12, 1  [#permalink]

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07 Jul 2017, 07:00
1
Bunuel wrote:
In the rectangular solid below, the three faces shown have areas 12, 15, and 20. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1800
(E) 3600

Attachment:
2017-07-07_1143.png

Let the sides of rectangular cuboid be $$= a , b,$$ and $$c$$

Given $$3$$ faces have areas $$= 12,15,$$ and $$20$$

$$a * b = 12$$

$$b * c =15$$

$$a * c = 20$$

Only sides $$3$$, $$4$$ and $$5$$ could have the above gives areas for each faces.

$$a = 3, b = 4 ,$$ and $$c = 5$$

Volume of rectangular cuboid $$= length * breadth * height$$

Volume of rectangular cuboid $$= a * b * c = 3 * 4 * 5 = 60$$

Re: In the rectangular solid below, the three faces shown have areas 12, 1   [#permalink] 07 Jul 2017, 07:00
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