Question 85

The surface area of a cube is 600 sq. cm. Its diagonal is

Solution

Let the side of cube = $$a$$ cm

=> Surface area = $$6 a^2 = 600$$

=> $$a^2 = \frac{600}{6} = 100$$

=> $$a = \sqrt{100} = 10$$ cm

Face diagonal of cube = $$\sqrt{10^2 + 10^2} = \sqrt{200} = 10 \sqrt{2}$$ cm

$$\therefore$$ Body diagonal = $$\sqrt{(10)^2 + (10 \sqrt{2})^2}$$

= $$\sqrt{100 + 200} = \sqrt{300} = 10 \sqrt{3}$$ cm

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