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# If the areas of three of the faces of a rectangular solid are 6, 10 an

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Math Expert
Joined: 02 Sep 2009
Posts: 52431
If the areas of three of the faces of a rectangular solid are 6, 10 an  [#permalink]

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30 Nov 2017, 22:02
00:00

Difficulty:

25% (medium)

Question Stats:

88% (00:57) correct 13% (01:21) wrong based on 38 sessions

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If the areas of three of the faces of a rectangular solid are 6, 10 and 15, what is the volume of the solid?

(A) 30
(B) 90
(C) 150
(D) 300
(E) 450

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Posts: 318
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Re: If the areas of three of the faces of a rectangular solid are 6, 10 an  [#permalink]

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30 Nov 2017, 22:05
2
A

Let l, b and h be the length, breadth and height of the rectangular solid respectively.

We have l*b=6
b*h=10
l*h=15

Multiplying all of the above we get (lbh)^2=900

Hence lbh=volume of rectangular solid =30

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Re: If the areas of three of the faces of a rectangular solid are 6, 10 an  [#permalink]

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01 Dec 2017, 10:24
Bunuel wrote:
If the areas of three of the faces of a rectangular solid are 6, 10 and 15, what is the volume of the solid?

(A) 30
(B) 90
(C) 150
(D) 300
(E) 450

Kudos to Sasindran - I used the approach for similar questions that do not involve volume.
Next time I will notice if volume is involved. Fortunately the numbers are easy.

Three surface areas of 6, 10, and 15

6 = 2 * 3
10 = 2 * 5
15 = 3 * 5

6 and 10 must share side with length 2
6 and 15 must share side with length 3
10 and 15 must share side with length 5

Volume = (L * H * W) = (5 * 2 * 3) = 30

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Posts: 318
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Concentration: Operations, Strategy
GPA: 3.73
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Re: If the areas of three of the faces of a rectangular solid are 6, 10 an  [#permalink]

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01 Dec 2017, 16:43
genxer123 wrote:
Bunuel wrote:
If the areas of three of the faces of a rectangular solid are 6, 10 and 15, what is the volume of the solid?

(A) 30
(B) 90
(C) 150
(D) 300
(E) 450

Kudos to Sasindran - I used the approach for similar questions that do not involve volume.
Next time I will notice if volume is involved. Fortunately the numbers are easy.

Three surface areas of 6, 10, and 15

6 = 2 * 3
10 = 2 * 5
15 = 3 * 5

6 and 10 must share side with length 2
6 and 15 must share side with length 3
10 and 15 must share side with length 5

Volume = (L * H * W) = (5 * 2 * 3) = 30

Thank you.

But I feel that your method is a little “trial and error” method.
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If the areas of three of the faces of a rectangular solid are 6, 10 an  [#permalink]

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01 Dec 2017, 21:41
Sasindran wrote:
genxer123 wrote:
Kudos to Sasindran - I used the approach for similar questions that do not involve volume. . . .
Next time I will notice if volume is involved.

Thank you.

But I feel that your method is a little “trial and error” method.

Sasindran , perhaps I was not clear. Or perhaps you misunderstood what I meant.

Your approach to this problem is vastly superior to mine. You were shrewd. I did not catch the algebraic connection. (Not good!)

And that meant I had to resort to finding the common side. I got lucky. As I mentioned, the numbers were easy. I will choose shrewd over lucky every time.

I put my method there for one reason only: I have seen questions where edge length must be found, and the only way to find edge length involves finding common sides. Those questions look a lot like this one.

That was my mistake. Your good work taught me that I got complacent. Here, yours is by far the better way, IMO.

Nice work.

(And next time, at least from me, please assume the best. If I go out of my way to name you in a compliment, that means I am thrilled to see someone do well and grateful to have learned something.) Cheers.
_________________

Sometimes at night I would sleep open-eyed underneath a sky dripping with stars.
I was alive then.

—Albert Camus

Senior Manager
Joined: 17 Oct 2016
Posts: 318
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: If the areas of three of the faces of a rectangular solid are 6, 10 an  [#permalink]

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01 Dec 2017, 22:29
genxer123 wrote:
Sasindran wrote:
genxer123 wrote:
Kudos to Sasindran - I used the approach for similar questions that do not involve volume. . . .
Next time I will notice if volume is involved.

Thank you.

But I feel that your method is a little “trial and error” method.

Sasindran , perhaps I was not clear. Or perhaps you misunderstood what I meant.

Your approach to this problem is vastly superior to mine. You were shrewd. I did not catch the algebraic connection. (Not good!)

And that meant I had to resort to finding the common side. I got lucky. As I mentioned, the numbers were easy. I will choose shrewd over lucky every time.

I put my method there for one reason only: I have seen questions where edge length must be found, and the only way to find edge length involves finding common sides. Those questions look a lot like this one.

That was my mistake. Your good work taught me that I got complacent. Here, yours is by far the better way, IMO.

Nice work.

(And next time, at least from me, please assume the best. If I go out of my way to name you in a compliment, that means I am thrilled to see someone do well and grateful to have learned something.) Cheers.

Thanks and good luck to you too

Posted from my mobile device
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Re: If the areas of three of the faces of a rectangular solid are 6, 10 an &nbs [#permalink] 01 Dec 2017, 22:29
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