Question

the Length breadth and height of a cuboid are in the ratio 7 ratio 6 ratio 5 if the surface area of the cuboid is 1926 CM square find its dimension also find the volume of the cuboid

Answer 1

Let the length of cuboid = 7x
Breadth of cuboid = 6x
Height of cuboid = 5x
The surface area of cuboid = 2(42x^2+30x^2+35x^2) = 1926
107x^2 = 1926/2
x^2 = 1926 / (2 x 107)
x^2 = 963/107
x^2 = 9
x = 3
Therefore, length = 21cm, breadth = 18cm & height = 15cm
Volume of cuboid = L x B x H
= 21x18x15
= 5670 cm^3

Answer 2

Let the length breadth and height of the cuboid be 7x, 6x and 5x respectively.
Now, total surface area of cuboid=
2(lb+bh+lh) = 1926cm (given)
[substituting the values]
2(lb+bh+lh) = 1926cm
2(7x*6x+6x*5x+7x*5x) =1926cm
2(42x^2+30x^2+35x^2) =1926cm
2*107x^2 =1926cm
214x^2 =1926cm
x^2 = 1926cm/214 = 9 cm
x =√9 cm
=3 cm

Now, Substituting 3 in place of x
7x = 7*3cm = 21 cm (length)
6x = 6*3cm = 18cm (breadth)
5x = 5*3cm = 15cm (height)

Volume of cuboid= (length*breadth*height)
= (21*18*15) cm= 5670 cm^3