The length of the diagonal of a cube is 6 tex | vedclass

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(B) The length of the diagonal of a cube is given by the formula $d = a\sqrt{3}$, where $a$ is the side length of the cube.Given that the diagonal $d

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(B) The length of the diagonal of a cube is given by the formula $d = a\sqrt{3}$, where $a$ is the side length of the cube.Given that the diagonal $d = 6 	ext{ cm}$.Therefore, $a\sqrt{3} = 6 	ext{ cm}$.Solving for $a$, we get $a = \frac{6}{\sqrt{3}} = \frac{6 	imes \sqrt{3}}{\sqrt{3} 	imes \sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3} 	ext{ cm}$.The volume $V$ of a cube is given by $V = a^3$.Substituting the value of $a$, we get $V = (2\sqrt{3})^3 = 2^3 	imes (\sqrt{3})^3 = 8 	imes 3\sqrt{3} = 24\sqrt{3} 	ext{ cm}^3$.

The length of the diagonal of a cube is $6 \text{ cm}$. The volume of the cube (in $\text{cm}^3$) is (in $\sqrt{3}$)

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