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The volume of a cuboid is 24 $m^{3}$ . Its length is 16 m, and its breadth and height are in a relation as 3:2. Its breadth is ____.

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Detailed Solution

The volume of a cuboid is 24

m^{3}

. Its length is 16 m, and its breadth and height are in a relation as 3:2. Its breadth is

\frac{3}{2}

m.
Given, the length of the cuboid is 16 m.
Breadth:height = 3:2
Let the breadth of the cuboid be x.
So the height is

\frac{2 x}{3}

.
We know that the volume of a cuboid is lbh =

16 \times x \times \frac{2 x}{3}

= \frac{32}{3} x^{2}

So,

\frac{32}{3} x^{2} = 24

x^{2} = \frac{72}{32}

x^{2} = \frac{36}{16}

x =

\frac{6}{4}

m
x =

\frac{3}{2}

m
Hence, the value of the breadth of the cuboid is

\frac{3}{2}

m.
Hence, the correct answer is

\frac{3}{2}

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