Question

The length, breadth and height of cuboid
are in the ratio 3 : 2:1. Its T.S.A is 550
cm? then its volume is​

Answer 1

Answer:

The Volume of the given cuboid is $750 cm^3$

Step-by-step explanation:

Let the Length, breadth and height of the Cuboid be 3x, 2x and x respectively.

It is given that the Total Surface Area of the Cuboid is $550cm^2$

So, we can say that,

$=>2[(3x*x)+(2x*x)+(3x*2x)] = 550\\=>2(3x^2+2x^2 +6x^2) = 550\\=>2(11x^2) = 550\\=>22x^2=550\\=>x^2 = 25\\=>x = 5cm$

So,

Length of the Cuboid $= 3x = 3*5 = 15cm$

Breadth of the Cuboid $= 2x = 2*5 = 10cm$

Height of the Cuboid $= x = 5 = 5cm$

Now,

We know that,

Volume of a Cuboid = Length * Breadth * Height

So,

Volume of the given cuboid $= 15 * 10 * 5 cm^3 = 750 cm^3$

Therefore, the Volume of the given cuboid is $750 cm^3$