Question

The breadth of the cuboid is 2 less than from its length and the height of the cuboid is 1 less than from its breadth and the surface area of the cuboid is 188msq. Find the volume of the cuboid.

Answer 1

Let,

Length of Cuboid, l = l cm

So, Breadth of Cuboid, b = ( l - 2 ) m

Also, Height of Cuboid, h = ( l - 2 ) - 1 = ( l - 3 ) m

T.S.A. of Cuboid = 188 m² ( given )

Also, T.S.A. of Cuboid = 2 ( lb + bh + hl)

•°•

2 ( lb + bh + hl ) = 188

lb + bh + hl = 188 / 2

lb + bh + hl = 94

Putting values

( l ) ( l - 2 ) + ( l - 2 ) ( l - 3 ) + ( l - 3 ) ( l ) = 94

l² - 2l + l² - 3l - 2l + 6 + l² - 3l = 94

3l² - 10l + 6 = 94

3l² - 10l + 6 - 94 = 0

3l² - 10l - 88 = 0

By Middle Term factorisation

3l² + 12l - 22l - 88 = 0

3l ( l + 4 ) - 22 ( l + 4 ) = 0

( 3l - 22 ) ( l + 4 ) = 0

Using Zero Product Rule

3l - 22 = 0 and l + 4 = 0

l = 22 / 3 and l = - 4

Length can't be negative.

So l ≠ - 4

Hence, Length = 22 / 3 m

Breadth = ( l - 2 ) = ( 22 / 3 ) - 2 = 16 / 3 m

Height = ( l - 3 ) = ( 22 / 3 ) - 3 = 13 / 3 m

Now,

Volume of Cuboid = lbh

= ( 22 / 3 ) ( 16 / 3 ) ( 13 / 3 )

= 169.48 m³