Question

the surface are of a cuboid is 1792 cm2 if its length, breadth and height are in the vation4:2:1 then find the length of the cuboid

Answer 1

Let the ratio of length, breadth , height be 4x , 2x , x

Given surface area of cuboid = 1792cm²

We know that,

Formula to find Surface area of cuboid is

→ 2( lb + bh + lh)

Here,

• l = length.
• b = breadth.
• h = height.

So,

→ 2( lb + bh + lh) = 1792cm²

Substituting the values, we get,

$\rm \dashrightarrow 2[4x(2x) + 2x(x) + x(4x)]= 1792cm^2$

$\rm \dashrightarrow 2(8x^2 + 2x^2 + 4x^2)= 1792cm^2$

$\rm \dashrightarrow 2(14x^2)= 1792cm^2$

$\rm \dashrightarrow x^2= \dfrac{1792cm^2}{2 \times 14}$

$\rm \dashrightarrow x^2= 64cm^2$

$\rm \dashrightarrow x= \sqrt{64cm^2}$

$\rm \dashrightarrow x= 8cm$

• Length = 4x = 4(8cm) = 32cm

• Breadth = 2x = 2(8cm) = 16cm

• Height = x = 8cm

Hence, length is 32cm.