Question

Find the volume of the box whose area of adjacent surface are 40m square,20m square and 8m square respectively

Answer 1

Answer:

Volume of box = 80m³

Step-by-step explanation:

Let the edges of the box be represented as a, b and c

=> Area of adjacent surfaces will be a*b, b*c and a*c

We are given that these areas are 40m², 20m² and 8m²

=> a*b = 40 ; b*c = 20 and a*c = 8

a*b = 40 => b = 40/a

b*c = 20 => c = 20/b

a*c = 8

=> a*(20/b) = 8

but b = 40/a

=> a*(20/(40/a)) = 8

=> a*(20a/40) = 8

=> a²/2 = 8

=> a² = 16

=> a = 4

On substituting, we get:

b = 40/a = 40/4 = 10

c = 8/a = 8/4 = 2

The edges of the box are 4m, 10m and 2m

=> Volume of box = 4*10*2 m³ = 80m³