Question

the dimensions of a cuboid are in the ratio 2:3:4 and it's total surface area is 5200cm^2
find the volume of the cuboid​

Answer 1

Let the dimensions be 2x , 3x and 4x .

Here ,

Length = 2x

Breadth = 3x

Height = 4x

We know that ,

TSA of cuboid = 2 (lb + bh + hl)

5200 = 2 [(2x × 3x) + (4x × 3x) + (4x × 2x)]

2600 = 6x² + 12x²  + 8x²

26x²  = 2600

x²  = 2600/26

x²  = 100

x = ± 10

But x cannot be negative .

Hence , x = 10 .

Length = 2x = 20 cm

Breadth = 3x = 30 cm

Height = 4x = 40 cm

Answer 2

Answer:

Let the dimensions of the cuboid be 2x, 3x and 4x, respectively.

As we know,

Total Surface Area of a cuboid = 2(lb + bh + hl)

Substituting the values:-

5200cm^2 = 2(2x*3x + 3x*4x + 4x*2x)

5200cm^2 = 2(6x^2 + 12x^2 + 8x^2)

5200cm^2 = 2(26x^2)

5200cm^2/2 = 26x^2

2600cm^2 = 26x^2

2600cm^2/26 = x^2

100cm^2 = x^2

10cm = x

So the value of x is 10cm.

Now,

Dimensions of cuboid are:-

2x = 2*10cm = 20cm

3x = 3*10cm = 30cm

4x = 4*10cm = 40cm

We know that,

Volume of a cuboid = l*b*h

Substituting the values:-

V = 20cm*30cm*40cm

V = 24000cm^3

Now,

1m^3 = 1000000cm^3

So,

24000cm^3 = 24000/1000000m^3

24000cm^3 = 0.024m^3

Hence, the volume of the cuboid is 24000cm^3 or 0.024m^3.