Question 82

What is the height of the cuboid, if the cube of diagonal 11√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 5.5 cm?

Solution

Let side of cube be $$a$$ cm

=> Diagonal = $$\sqrt{a^2+a^2+a^2}=11\sqrt3$$

=> $$\sqrt3a=11\sqrt3$$

=> $$a=11$$ cm

Let height of cuboid = $$h$$ cm, length, $$l=11$$ cm and breadth, $$b=5.5$$ cm

According to ques, Volume of cuboid = Volume of cube

=> $$lbh=a^3$$

=> $$11\times5.5\times h=(11)^3$$

=> $$h=\frac{11\times11}{5.5}=22$$ cm

=> Ans - (C)

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