Question

The dimensions of a rectangular box are in the ratio 5:4:2. Its total surface area is 7.600 cm Find the dimensions of the box and also its volume​

Answer 1

The dimensions of a rectangular box are in the ratio 5:4:2. Its total surface area is 7.600 cm Find the dimensions of the box and also its volume

Ratio = 5:4:2

Total surface area ,= 7600 cm

Let dimension of cuboid art be ,

l=5x

b=4x

h=2x

Surface area of cuboid = 7600

( After calculation x = 10 )

Dimension of cuboid

l = 50 cm

b = 40 cm

h = 20 cm

volume = l×b×h

= 40000 cm³

Answer 2

Given :

Dimensions of a Rectangular Box are in the ration 5 : 4 : 2

Total Surface Area = 7600 cm²

To Find :

Dimensions of the Box

Volume of the Box

Solution :

Let the Dimensions be 5y , 4y , 2y

By using,

$\boxed{ \color{gold}\bf Total \: \: Surface \: \: Area = 2(lb + bh + hl)}$

⇒ TSA = 2(5y.4y + 4y.2y + 5y.2y)

⇒ 7600 = 76y²

⇒ y² = 100

⇒ y = 10

Then, Dimensions are :

5y = 5(10) = 50cm

4y = 4(10) = 40cm

2y = 2(10) = 20cm

Volume of Cuboid is calculated by using,

$\boxed{ \color{brown} \bf Volume \: of \: Cuboid = lbh}$

⇒ Volume = 50 x 40 x 20

⇒ Volume = 4000 cm³

FINAL ANSWER :

Volume = 4000cm³

dimensions ARE : 50cm , 40cm , 20cm