QZ wrote:

The volume of a cube with edge \(3\) is how many times the volume of a cube with edge \(\sqrt{3}\)?

a. \(\frac{1}{3}\)

b. \(1\)

c. \(3\)

d. \(3\sqrt{3}\)

e. \(9\)

I. Volume/VolumeVolume of a cube =

\(s^3\)Volume of smaller cube =

\((\sqrt{3})^3 = 3\sqrt{3}\)Volume of larger cube =

\(3^3 = 27\)Volume of \(27\) is how many times greater than \(3\sqrt{3}\)?

\(\frac{27}{3\sqrt{3}} =\)

\(\frac{27}{3\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}}=\)

\(\frac{27\sqrt{3}}{9} = 3\sqrt{3}\)ANSWER DII. Cube the scale factor• SCALE FACTOR: If a shape's size increases or decreases, it scales up or scales down.

That means that every length in the shape has been multiplied by a scale factor, \(k\)

The scale factor is a multiplier; any change in length =

length * scale factor \(k\)Scale factors tell you "how many times"

the smaller size was multiplied to obtain the greater size

You need nothing else in this problem except (scale factor)\(^3\)

• To account for change in length, area, or volume:

Length = \(k\)

Area = (length * length) = \(k^2\)

Volume= (length * length * length) =

\(k^3\)• Scale factor here?

Use ONE length's increase to find \(k\):

\((k) * (s\) of small cube) =

(\(s\) of large cube)

Scale factor EQUALS?*

Small cube's side length:

\(\sqrt{3}\)Large cube's side length = 3

\(k * \sqrt{3} = 3\)

\(\sqrt{3}*\sqrt{3} = 3\)

\(k = \sqrt{3}\)Volume increase? \(k^3\)

To find out "how many times greater," because it's a volume change --

cube the scale factor \((\sqrt{3})^3 = (\sqrt{3} * \sqrt{3} * \sqrt{3}) = 3\sqrt{3}\)The volume of a cube with edge \(3\) is \(3\sqrt{3}\) times the volume of a cube with edge \(\sqrt{3}\)

Answer D*

Or \(k * \sqrt{3} = 3\)

\(k = \frac{3}{\sqrt{3}}\)

\(k = \frac{3}{\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}}\)

\(k=\frac{3\sqrt{3}}{3}=\sqrt{3}\)
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