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If segment QR in the cube below has length 4 3 inches, what is the vol

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Bunuel
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If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink] New post   05 Dec 2014, 07:36
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Tough and Tricky questions: Geometry.



If segment QR in the cube below has length \(4\sqrt{3}\) inches, what is the volume of the cube (in cubic inches)?
Attachment:
2014-12-05_1835.png
2014-12-05_1835.png [ 3.18 KiB | Viewed 3255 times ]


A) 16
B) 27
C) 64
D) 81
E) 125

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C
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Re: If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink] New post   05 Dec 2014, 10:59
I'm not sure if there's a typo in the question or not. I assumed that segment QR in the cube had a length of 4.3 and not 43 inches. So, let's begin.

First of all, recognize that segment QR is a cube diagonal, which means its length is always equal to side*sqrt(3). From this, each cube side length equals 4.3/sqrt(3). To get the volume, cube this value. Let's simplify the side by saying it equals 4.3/1.7, which is ~2.5.

Now 2.5^3 is between 2^3 = 8 and 3^3 = 27. So, I picked A--a volume of 16.

Now if the diagonal is supposed to be 4*sqrt(3), the problem is made much simpler, by yielding a side length of 4 and a cube volume of 64. Choice C

Bunuel, can you please clarify.
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Re: If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink] New post   05 Dec 2014, 14:22
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If segment QR in the cube has length \(4*\sqrt{3}\) inches, what is the volume of the cube (in cubic inches)?

A) 16
B) 27
C) 64
D) 81
E) 125


Volume of the cube = \({(\frac{Segment QR}{\sqrt{3}})}^3\)

= \({(4*\sqrt{3}/\sqrt{3})}^3\)

=\(64\) cubic inches

Answer: C
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Re: If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink] New post   06 Dec 2014, 08:03
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Let the length of each side = a
length of QR= sq. rt 3a*a=4*sr rt 3
squaring both sides
3a^2=16*3=64
a^2=16
a=4
volume =a^3=64.
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Re: If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink] New post   08 Dec 2014, 06:07
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Bunuel wrote:

Tough and Tricky questions: Geometry.



If segment QR in the cube below has length 4 3 inches, what is the volume of the cube (in cubic inches)?
Attachment:
2014-12-05_1835.png


A) 16
B) 27
C) 64
D) 81
E) 125

Kudos for a correct solution.

Source: Chili Hot GMAT


The correct answer is C.
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Re: If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink] New post   08 Dec 2014, 21:22
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Bunuel wrote:

Tough and Tricky questions: Geometry.



If segment QR in the cube below has length 4 3 inches, what is the volume of the cube (in cubic inches)?
Attachment:
2014-12-05_1835.png


A) 16
B) 27
C) 64
D) 81
E) 125

Kudos for a correct solution.

Source: Chili Hot GMAT


Bunuel, kindly update the question....

Length \(= 4\sqrt{3}\) inches
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If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink] New post   27 Jan 2016, 02:26
Denote side by a.

\({QR}^2\)= \({a}^2\) +\({Diag. of Base Aquare}^2\)

Diag. of Base Square = \(\sqrt{({a}^2+{a}^2)}\) = \(\sqrt{2}a\)
\({QR}^2\) = \({a}^2\) +2\({a}^2\)
= \(3{a}^2\)
QR = \(\sqrt{3}a\)

\(4* \sqrt{3}\) = \(\sqrt{3}a\)
=>a = 4

Volume of the cube = \({a}^3\)
=\({4}^3\)
=64
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Re: If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink] New post   11 Sep 2020, 23:04
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Re: If segment QR in the cube below has length 4 3 inches, what is the vol [#permalink]
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