Question 109

What is the height of the cuboid, if the cube of diagonal 47√3cm is melted and casted, the cuboid’s length is the same as the cube’s side and the breadth of the cuboid is 23.5cm? (in cm)

Solution

Let side of cube be $$a$$ cm

=> Diagonal = $$\sqrt{a^2+a^2+a^2}=47\sqrt3$$

=> $$\sqrt3a=47\sqrt3$$

=> $$a=47$$ cm

Let height of cuboid = $$h$$ cm, length, $$l=47$$ cm and breadth, $$b=23.5$$ cm

According to ques, Volume of cuboid = Volume of cube

=> $$lbh=a^3$$

=> $$47\times23.5\times h=(47)^3$$

=> $$h=\frac{47\times47}{23.5}=94$$ cm

=> Ans - (A)

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