There is a rectangular solid. The areas of faces are 8,

Question

There is a rectangular solid.

The areas of faces are 8, 24, and 27.

What is the volume of this rectangular solid?

remgeo · Answer

length * breadth = 27
breadth * height = 24
length * height = 8


volume = length * breadth * height = sqrt(27 * 24 * 8) = 

sqrt ( 3* 3 * 3 * 8 * 8 * 3 * 8) = 8*3*3

= 72

remgeo · Answer

A solid has 6 faces out of which the opposite faces are of equal area. So there are 3 different faces which have areas 27, 24, 8. 

ie. l*b = 27
 l* h = 24
 h * b = 8

Multiplying all of the above, 
l * h * b * l * b * h = 27 * 24 * 8

ie. l^2*b^2*c^2 = 27*24*8
Therefore lbh = sqrt(27*24*8) = 72

christoph · Answer

ok, then sides may be 8,3,3. when u multiply them u dont get 27 as an area. in your case the 3 diff areas are 9 24 24. thats diff from 27 24 8.

GMATT73 · Answer

I also thought the same thing at first Christof, but after thorough introspection and support from the Q master, Remgeo appears to be correct. 
I even did the brute force math and multiplied sqrt(27*24*8)=sqrt(5184) or 72.

laxieqv · Answer

you'd better not assign h, width, l to the area...better to use a,b,c generally so that the problem is considered comprehensively :wink:

christoph · Answer

so then the values of the sides are not integers ?

GMATT73 · Answer

Yup! That wasn`t specified in the problem. Like Hjort proclaimed and HIMALAYA reminded me last week:  assume nothing.

christoph · Answer

<img src="{SMILIES_PATH}/080402argh_prv.gif" alt=":arh" title="Mad" />

remgeo · Answer

I can see that my daft explanation has created some stir :shock:

As you have already seen, I'm no good at it.. but I'll try :wink:

nakib77 · Answer

let me try and explain it.

are of the faces are : hight* length
 length*width
 width *hight

and volume of the solid =hight* width* length

so if we multiply all the faces we get hight^2*width^2* length^2

so in order to get the volume all we need to do is sqrt(8*24*27)
= sqrt( 8*8*3*3*9)
= 8*9=72

so 72 is the answer. hope it explains.

There is a rectangular solid. The areas of faces are 8,

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