Question 52

The diagonal of a cube is $$\sqrt{192}$$ cm. Its volume is $$(cm^{3})$$ will be

Solution

Let side of cube = $$a$$ cm

=> Diagonal of cube = $$\sqrt3a$$ cm

=> $$\sqrt3a=\sqrt{192}$$

=> $$a=\sqrt{\frac{192}{3}}=\sqrt{64}$$

=> $$a=8$$ cm

$$\therefore$$ Volume of cube = $$(a)^3$$

= $$(8)^3=512$$ $$cm^3$$

=> Ans - (C)

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