Question 88

What is the height of the cuboid, if the cube of diagonal 44√3cm is melted and casted, the cuboid’s length is the same as the cube’s side and the breadth of the cuboid is 22cm? (in cm)

Let side of cube be $$a$$ cm

=> Diagonal = $$\sqrt{a^2+a^2+a^2}=44\sqrt3$$

=> $$\sqrt3a=44\sqrt3$$

=> $$a=44$$ cm

Let height of cuboid = $$h$$ cm, length, $$l=44$$ cm and breadth, $$b=22$$ cm

According to ques, Volume of cuboid = Volume of cube

=> $$lbh=a^3$$

=> $$44\times22\times h=(44)^3$$

=> $$h=\frac{44\times44}{22}=88$$ cm

=> Ans - (C)

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