Question 110

# What is the height of the cuboid, if the cube of diagonal 22√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 11 cm? (in cm)

Solution

Let side of cube be $$a$$ cm

=> Diagonal = $$\sqrt{a^2+a^2+a^2}=22\sqrt3$$

=> $$\sqrt3a=22\sqrt3$$

=> $$a=22$$ cm

Let height of cuboid = $$h$$ cm, length, $$l=22$$ cm and breadth, $$b=11$$ cm

According to ques, Volume of cuboid = Volume of cube

=> $$lbh=a^3$$

=> $$22\times11\times h=(22)^3$$

=> $$h=\frac{22\times22}{11}=44$$ cm

=> Ans - (B)