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# The figure above represents a box that has the shape of a cube. What i

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The figure above represents a box that has the shape of a cube. What i  [#permalink]

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26 Apr 2019, 03:12
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The figure above represents a box that has the shape of a cube. What is the volume of the box?

(1) PR = 10 cm
(2) $$QT = 5\sqrt{6}$$ cm

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26 Apr 2019, 04:37
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The figure above represents a box that has the shape of a cube. What is the volume of the box?
Any regular figure, that is any figure with all sides equal, will just require any one dimension, length, diagonal, altitude, area or volume to know the remaining as all are based on one variable, that is side.
Same is the case here in cube.

(1) PR = 10 cm
Diagonal of a side is known-> sides can be known-> volume can be calculated.
side = $$5\sqrt{2}$$.. Volume = $$(5\sqrt{2})^3$$.

(2) $$QT = 5\sqrt{6}$$ cm
QT is the diagonal of cube = $$\sqrt{3*side^2}=side\sqrt{3}=5\sqrt{6}...side=$$ $$5\sqrt{2}$$.. Volume = $$(5\sqrt{2})^3$$.

D
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Re: The figure above represents a box that has the shape of a cube. What i  [#permalink]

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27 Apr 2019, 13:55
The Logical approach to this question is simple and extremely fast: when it comes to regular solids - just like regular polygons - any given measurement (side, diagonal, surface area, volume, etc.) is enough on order to find any other measurement. Thus, since both statements provide such measurements, they each suffice on their own and the correct answer is (D).

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Re: The figure above represents a box that has the shape of a cube. What i  [#permalink]

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09 May 2019, 07:19
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Bunuel wrote:

The figure above represents a box that has the shape of a cube. What is the volume of the box?

(1) PR = 10 cm
(2) QT = 5√6 cm
Attachment:
2019-04-26_1410.png

Target question: What is the volume of the box?

IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement.
This concept is discussed in much greater detail in the video below.

This technique can save a lot of time.

Notice that there are infinitely-many cubes...

...and, for each cube, we have different measurements for PR and QT, AND each one of these unique cubes has its very own volume.
So, if a statement LOCKS in the precise measurements of the cube, then that statement must be sufficient.

Statement 1: PR = 10 cm
Among the infinitely-many cubes that exist in the universe, ONLY ONE cube is such that PR = 10 cm
Since statement 1 locks in the size of the cube, it is SUFFICIENT

Statement 2: QT = 5√6 cm
Among the infinitely-many cubes that exist in the universe, ONLY ONE cube is such that QT = 5√6 cmcm
Since statement 2 locks in the size of the cube, it is SUFFICIENT

Cheers,
Brent

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Re: The figure above represents a box that has the shape of a cube. What i  [#permalink]

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09 May 2019, 12:36
chetan2u wrote:

The figure above represents a box that has the shape of a cube. What is the volume of the box?
Any regular figure, that is any figure with all sides equal, will just require any one dimension, length, diagonal, altitude, area or volume to know the remaining as all are based on one variable, that is side.
Same is the case here in cube.

(1) PR = 10 cm
Diagonal of a side is known-> sides can be known-> volume can be calculated.
side = $$5\sqrt{2}$$.. Volume = $$(5\sqrt{2})^3$$.

(2) $$QT = 5\sqrt{6}$$ cm
QT is the diagonal of cube = $$\sqrt{3*side^2}=side\sqrt{3}=5\sqrt{6}...side=$$ $$5\sqrt{2}$$.. Volume = $$(5\sqrt{2})^3$$.

D

could you kindly elaborate on the equation more please?
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Re: The figure above represents a box that has the shape of a cube. What i  [#permalink]

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09 May 2019, 17:29
Hi All,

We're told that the figure above represents a box that has the shape of a CUBE. We're asked for the is the volume of the cube. While this question might appear a bit 'scary', there's a great 'logic shortcut' built into it - since we're dealing with a CUBE, we know that all of the dimensions are EQUAL. By extension, if we know ANY length connecting two of the 8 vertices on the cube, then we can figure out ALL of the other lengths (using other Geometry formulas, although we won't actually have to do any of that math here) - and ultimately determine the volume.

1) PR = 10 cm

Length PR is a diagonal that forms on each face of the cube, so it would be the hypotenuse of a 45/45/90 right triangle. With that measurement, we could calculate the exact values of the sides and calculate the volume. There would be only one answer.

Fact 1 is SUFFICIENT

2) QT = 5√6 cm

When dealing with a 'rectangular solid', the formula for calculating the length from one 'corner' of the shape to the 'opposite opposite' corner is:
√(L^2 + W^2 + H^2)

Since we're dealing with a cube, we know that the length, width and height are the SAME. We can refer to all of those lengths as "X", which gives us:
√(X^2 + X^2 + X^2) = √(3X^2) = 5√6

With one variable and one equation, we CAN solve for the value of X - and there would be just one value, so we could calculate the volume of the cube.
Fact 2 is SUFFICIENT

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Re: The figure above represents a box that has the shape of a cube. What i   [#permalink] 09 May 2019, 17:29
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