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.

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Solution

It is given that

Volume of cuboid $= 1536 m^{3}$

Length of cuboid $= 16 m$

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

We know that

Volume of cuboid $= 1 \times b \times h$

By substituting the value

$1536 = 16 \times 3 x \times 2 x$

On further calculation

$1536 = 96 x^{2}$

So we get

$x^{2} = \frac{1536}{96}$

$x^{2} = 16$

By taking the square root

$x = \sqrt{16}$

We get

$x = 4 m$

Substituting the value of $x$

Breadth of cuboid $= 3 x = 3 (4) = 12 m$

Height of cuboid $= 2 x = 2 (4) = 8 m$

Therefore, the breadth of the height of the cuboid are $12 m$ and $8 m$ .

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The volume of a cuboid is 1536 m3. Its length is 16 m, and its breadth and height are in the ratio 3:2. Find the breadth and height of the cuboid.

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.