Question

The volume of a cuboid is 1372 cm³. Its breadth is equal to its length and its height is 4 times its width. What are the dimensions of the cuboid?

Answer 1

Answer:

Length=x=7cm

Breath=x=7cm

Height=4x=28cm

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Answer 2

Breath of the cuboid = 7 cm

length of the cuboid = 7 cm

Height of the cuboid = 4× 7 = 28 cm

GIVEN

The volume of the cuboid = 1372 cm³

Breath of the cuboid = Length of the cuboid.

Height of the cuboid = 4 × breath

TO FIND

Dimension of the cuboid.

SOLUTION

We can simply solve the above problem as under -

Let the breath of the cuboid be, x

so, the length will also be, x

Height = 4 × breath = 4x

It is given,

The volume of the cuboid = 1372 cm³

we know,

The volume of the cube = l × b × h

Where,

l = length of the cube

b = breath of the cube

h = height of the cube.

Putting the values in the above formula we get,

$x \times x \times 4x = 1372$

$4 {x}^{3} = 1372$

${x}^{3} = \frac{1372}{4} = 343$

$x = \sqrt[3]{343}$

x = 7

Hence,

Breath of the cuboid = 7 cm

length of the cuboid = 7 cm

Height of the cuboid = 4× 7 = 28 cm

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