If the cube with a 45√3 cm diagonal is molded, the side of the cube and the length of the cuboid is the same size. If the width of the cuboid is 22.5 cm, what is its height? (In centimeters)
Solution
Let side of cube be $$a$$ cm
=> Diagonal = $$\sqrt{a^2+a^2+a^2}=45\sqrt3$$
=> $$\sqrt3a=45\sqrt3$$
=> $$a=45$$ cm
Let height of cuboid = $$h$$ cm, length, $$l=45$$ cm and breadth, $$b=22.5$$ cm
According to ques, Volume of cuboid = Volume of cube
=> $$lbh=a^3$$
=> $$45\times22.5\times h=(45)^3$$
=> $$h=\frac{45\times45}{22.5}=90$$ cm
=> Ans - (C)
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