Question

the dimensions of a cuboid are in the ratio of 4 ratio 3 ratio 1 if its total surface area is 3800 CM square then find its volume ​

Answer 1

Answer:12000 cubic units

Step-by-step explanation:

Let the common ratio of sides be x.

So sides are 4x, 3x, and x (l, b and h)

Total Surface Area = 3800 = 2(lb+bh+hl)

3800/2 = (4x.3x + 4x.x + 3x.x) ('.' means multiply)

1900 = 12x^{2} + 4x^{2} + 3x^{2}

1900 = 19x^{2}

x^{2} = 100

so x = 10

so sides are 10, 30 and 40 units

volume = 10 x 30 x 40 cubic units

= 12,000 cubic units

Answer 2

Answer:

The Volume of cuboid is 1200 cubic centimeter .

Step-by-step explanation:

Given as :

The Total Surface Area of cuboid = 3800 sq cm

Let The length = 4 x

Breadth = 3 x

height = x

So, Toal Surface Area = 2 ( LB + BH + HL)

Or, 3800 = 2 (4 x × 3 x + 3 x × x + x × 4 x )

Or, $\dfrac{3800}{2}$ =  ( 12 x² + 3 x² + 4 x² )

or, 19 x² = 1900

Or, x² = $\dfrac{1900}{19}$

or, x² = 100

Or, x = √100  = 10

So, The length = 4 × 10 = 40

Breadth = 3 × 10 = 30

height = 10

Now, Volume of cuboid = L × B × H

                                       = 40 × 30 × 10

∴  , Volume of cuboid = 1200 cubic cm

Hence, The Volume of cuboid is 1200 cubic centimeter . Answer