Question

the edges of cuboid are in the ratio of 1 ratio 2 ratio 3 and its surface area is 88 CM square what will be the volume of the cuboid? ​

Answer 1

Given that,

• The ratio of Length, Breadth and Height is 1 : 2 : 3.
• The Surface Area of the Cuboid.

To Find,

• The Volume of the Cuboid.

Solution,

Let the Length ( l ) of Cuboid be 'x',

The Breadth ( b ) of Cuboid should be '2x',

And, The Height ( h ) of Cuboid should be '3x'.

As we know,

• The T.S.A. of the Cuboid = 2( lb + bh + hl )

Substituting the values,

• •➤ 2( lb + bh + hl ) = 88cm²
• •➤ x(2x) + 2x(3x) + 3x(x) = 44cm²
• •➤ 2x² + 6x² + 3x² = 44cm²
• •➤ 11x² = 44cm²
• •➤ x² = 4cm²
• •➤ x = 2cm

Hence, The value of 'x'is 2cm.

We found,

• The Length of the Cuboid is 2cm,
• The Breadth of the Cuboid is 4cm [2(2) = 4],

And,

• The Height of the Cuboid is 6cm [3(2) = 6].

As we know,

• Volume of Cuboid = lbh

Substituting the found values,

• •➤ Volume = 2cm × 4cm × 6cm
• •➤ Volume = 48cm³

Therefore, The Volume of Cuboid is 48cm³.

Required Answer,

• The Volume of Cuboid is 48 cubic cms.