Question

# The volume of a cuboid is $$1536\ m^{3}$$. Its length is $$16\ m$$, and its breadth and height are in the ratio $$3:2$$. Find the breadth and height of the cuboid.

Solution

## It is given thatVolume of cuboid $$=1536\ m^3$$Length of cuboid $$=16m$$Consider breadth as $$3x$$ and height $$2x$$We know thatVolume of cuboid $$=1\times b\times h$$By substituting the value$$1536=16\times 3x\times 2x$$On further calculation$$1536=96x^2$$So we get$$x^2 =\dfrac{1536}{96}$$$$x^2 =16$$By taking the square root$$x=\sqrt {16}$$We get$$x=4m$$Substituting the value of $$x$$Breadth of cuboid $$=3x=3(4)=12m$$Height of cuboid $$=2x=2(4)=8m$$Therefore, the breadth of the height of the cuboid are $$12m$$ and $$8m$$.MathematicsRS AgarwalStandard IX

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