Question

The volume of a cuboid is 3840 cm³ and the length of the cuboid is 20 cm. If the ratio of its breadth and its height is 4 : 3, then the total surface area of the cuboid is __________.

Answer 1

Length of the cuboid, l = 20 cm

Let b and h be the breadth and height of the cuboid, respectively.

Breadth of the cuboid, b = 4x

Height of the cuboid, h = 3x

It is given that, the volume of a cuboid is 3840 cm³.

$\therefore l\times b\times h=3840{\mathrm{cm}}^3$

$\Rightarrow 20\times 4x\times 3x=3840$

$\Rightarrow x^2=16$

$\Rightarrow x=4\mathrm{cm}$

So,

Breadth of the cuboid, b = 4x = 4 × 4 cm = 16 cm

Height of the cuboid, h = 3x = 3 × 4 cm = 12 cm

∴ Total surface area of the cuboid

= 2(lb + bh + hl)

= 2(20 × 16 + 16 × 12 + 12 × 20)

= 2 × 752

= 1504 cm²

Thus, the total surface area of the cuboid is 1504 cm².

The volume of a cuboid is 3840 cm³ and the length of the cuboid is 20 cm. If the ratio of its breadth and its height is 4 : 3, then the total surface area of the cuboid is $\underline{1504{\mathrm{cm}}^2}$.