Question

the edges of a cuboid are in the ratio 1:2:3 and its surface area is 198 sq.cm find the volume of the cuboid

Answer 1

the answer is in the image

Answer 2

Given,

The ratio of the edges of a cuboid = 1:2:3,

The surface area of the cuboid is 198 cm².

To find,

The volume of the cuboid.

Solution,

The edges of the cuboid are given to be in the ratio = 1:2:3.

Firstly, let the edges of the cuboid be x, 2x, and 3x such that

length, l = x,

breadth, b = 2x, and,

height, h= 3x.

Now, since the surface area of a cuboid (S) is given by the formula,

S = 2(lb + bh + hl)

For the given cuboid, S = 198 cm², hence,

2(l·b + b·h + h·l) = 198

⇒ 2[(x)·(2x) + (2x)·(3x) + (3x)·(x)] = 198

⇒ 2[2x² + 6x² + 3x²] = 198

⇒ 2[11x²] = 198

⇒ 22x² = 198

⇒ x² = 9

⇒ x = 3.

Now, the dimensions of the cuboid can be found as follows.

l = x = 3 cm,

b = 2x = 2(3) = 6 cm, and,

h = 3x = 3(3) = 9 cm.

So, the volume of the cuboid,

V = l·b·h

⇒ V = (3)(6)(9)

⇒ V = 162 cm³.

Therefore, the volume of the given cuboid will be 162 cm³.