Question

The dimensions of a cuboid are in the ratio 5 : 2 : 1 . It's volume is 1250 cubic meters. What is its total surface area?

Answer 1

Let the length, breath ,height be
5x,2x,x

5x.2x.x=1250
$10 {x}^{3} = 1250$
x =5

dimensions are 25,10,5

Answer 2

We know that the dimensions of the cuboid are in the ratio 5 : 2 : 1, meaning they can be represented as 5k : 2k : 1k.

Since the volume of a cuboid is

V = L*W*H

we can replace the three dimensions with our three unknown dimensional terms:  

V = 5k*2k*1k = 1250 $m^{3}$

10$k^{3}$^3 = 1250

$k^{3}$ = 125

k = $\sqrt[3]{125}$

k = 5

∴ 5*5 : 2*5 : 1*5  =  (125 : 10 : 5)

Surface Area of cuboid is-

SA = 2 * (L*W + L*H + W*H)

SA = 2 * [(25)*(10) + (25)*(5) + (10)*(5)]

SA = 2 * [250 + 125 + 50]

∴  SA = 850 $m^{3}$