Question 36

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

Solution

let the length of the edge of the cube be a

diagonal of cube = $$ a \sqrt{3} $$

given diagonal = 6cm

$$a \sqrt{3} = 6 $$

$$ a = \frac{6}{\sqrt{3} = 2 \sqrt{3} $$

$$ Volume of cube = a^3 $$

V = $$ (2\sqrt{3})^3 = 24 \sqrt{3} $$

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