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# What is the volume of a certain rectangular solid?

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Manager
Joined: 30 Jan 2006
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What is the volume of a certain rectangular solid? [#permalink]

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14 Dec 2007, 09:02
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Q. What is the volume of a certain rectangular solid?
(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.

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Director
Joined: 12 Jul 2007
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14 Dec 2007, 09:55

A rectangular solid has 6 sides and each side has the same dimensions/area as the side opposite to it.

http://www.durangobill.com/IntBrick2.gif (link if the picture isn't working)

Here's a picture to help visualize it. (the numbers in the picture mean nothing, just using it to visualize the shape and how the sides interact)

1. Two adjacent sides have areas 15 and 24

doesn't help us, we need all the dimensions

2. Each of two opposite faces has area 40

doesn't help us on it's own,

but together it tells us that the 3 pairs of sides have areas 15, 24 and 40

now we write up a formula

xy = 15
xz = 24 (x is in both because they're adjacent and share a side)
yz = 40 (the last side is made up of one side of each of the other ones

x=(15/y)
z = (40/y)
xz = 24 so (15/y)(40/y) = 24

600/y^2 = 24
600=24y^2
25 = y^2
y = 5

plug in 5 for y and you get the rest

5x = 15 so x = 3
5z = 40 so z = 8

sides are 3, 5 and 8

volume = 3*5*8 = 120

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CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4672 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: Rectangular Solid - DS [#permalink]

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14 Dec 2007, 14:33
B

(2) Each of two opposite faces of the solid has area 40. - this means that each face of the rectangular solid has area 40.

a*b=40
b*c=40
c*a=40

where a,b,c - edges of the rectangular solid.

write: (a*b)*(b*c)*(c*a)=40³ ==> (a*b*c)²=40³ ==> V²=40³ ==>
V=√40³

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Director
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14 Dec 2007, 14:50
Quote:
(2) Each of two opposite faces of the solid has area 40. - this means that each face of the rectangular solid has area 40.

The figure in question is a rectangular solid, not a cube. Just because two of the sides have an area of 40 doesn't mean that every side as an area of solid.

Since it's a rectangular solid the information in statements 1 and 2 can both exist at the same time. two pieces have an area of 15, two have an area of 24 and two have an area of 40.

Look at the rectangle in the diagram:

85*132 = area of end piece
720*85 = area of side piece
720*132 = area of top piece

There's a rectangle with 6 sides and 2 sides of one area, 2 sides of another area and the last 2 have a yet another area.[/quote]

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CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4672 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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14 Dec 2007, 15:08
eschn3am wrote:
The figure in question is a rectangular solid, not a cube.

a cube is a rectangular solid....

One of us has been caught by GMAT

What's OA?

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Intern
Joined: 13 Jun 2007
Posts: 48

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14 Dec 2007, 15:26
C for me.
The question says "each of two" not "each of any two" so we cannot assume that it is a cube

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CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4672 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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14 Dec 2007, 15:39

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Director
Joined: 12 Jul 2007
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14 Dec 2007, 15:49
All cubes are rectangular solids...but not all rectangular solids are cubes. This is the kind of thing that makes the GMAT so tricky

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14 Dec 2007, 15:49
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