Question 130

A cuboid of sides 5 cm, 10 cm and 20 cm are melted to form a new cube. What is the ratio between the total surface area of the cuboid and that of the cube?

Solution

Let edge of cube = $$a$$ cm

Now, volume of cube = Volume of cuboid

=> $$a^3=5\times10\times20$$

=> $$a=\sqrt[3]{1000}=10$$ cm

Ratio between the total surface area of the cuboid and that of the cube = $$\frac{2(lb+bh+hl)}{6a^2}$$

= $$\frac{2[(5\times10)+(10\times20)+(20\times5)]}{6\times(10)^2}$$

=> $$\frac{2\times(50+200+100)}{600}=\frac{700}{600}=\frac{7}{6}$$

=> Ans - (B)

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