Edges of a cuboid are in the ratio 1 : 2 : 3. Its surface area is 88 cm². What is its volume?

The ratio of the edges of the cuboid is 1:2:3.

Surface area = 88 cm².

Let the dimensions of the cuboid be:

Length = x,

Width = 2x,

Height = 3x.

Surface Area of a cuboid:

Surface Area=2(lb+bh+hl)

where l is the length, b is the width, and h is the height.

Volume of a cuboid:

Volume=l×b×h

Let the dimensions of the cuboid be:

Length = x, breadth = 2x, Height = 3x.

Then,

​$$\begin{aligned}&88 = 2 \left[ x(2x) + (2x)(3x) + (3x)(x) \right] \\&88 = 2 \left( 2x^2 + 6x^2 + 3x^2 \right) \\&88 = 2 \times 11x^2 \\&88 = 22x^2 \\&x^2 = \frac{88}{22} \\&x = \sqrt{4} ​= 2 \\& \text{Volume} = l \times b \times h = x \times 2x \times 3x = 2 \times 4 \times 6 = 48 \text{cm}^3 \end{aligned}$$​​

Therefore, the volume of the cuboid is 48 cm³.