Question 100

What is the height of the cuboid, if the cube of diagonal 6√3 cm is melted and casted, the cuboid’s length is the same as the cube’s side and the breadth of the cuboid is 3 cm?

Solution

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Let side of cube be $$a$$ cm

=> Diagonal = $$\sqrt{a^2+a^2+a^2}=6\sqrt3$$

=> $$\sqrt3a=6\sqrt3$$

=> $$a=6$$ cm

Let height of cuboid = $$h$$ cm, length, $$l=6$$ cm and breadth, $$b=3$$ cm

According to ques, Volume of cuboid = Volume of cube

=> $$lbh=a^3$$

=> $$6\times3\times h=(6)^3$$

=> $$h=\frac{6\times6}{3}=12$$ cm

=> Ans - (B)

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