Question

What is the volume of a cube (in cm)³ whose diagonal measures 4√3cm​

Answer 1

Answer:

volume = 192 cm^3

Step-by-step explanation:

volume = root 3 diagonal cube / 9

diagonal cube = 576root 3

thus volume = 1728 / 9

= 192 cm^3

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Answer 2

Answer:

$64c {m}^{3}$

Step-by-step explanation:

Volume of Cube when diagonal is given

$v = \sqrt{3} \frac{ {d}^{3} }{9}$

$d = 4 \sqrt{3}$

${d}^{3} = {(4 \sqrt{3}) }^{3} \\ = 192 \sqrt{3}$

$= \sqrt{3} \frac{192 \sqrt{3} }{9} \\ = \frac{192 \times 3}{9} \\ = \frac{192}{3} \\ = 64 \: c {m}^{3}$