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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 that

Volume of cuboid $$=1536\ m^3$$

Length of cuboid $$=16m$$

Consider breadth as $$3x$$ and height $$2x$$

We know that

Volume 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 $$8m$$.

Mathematics
RS Agarwal
Standard IX

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