how to find the dimensions of this cuboid

Question

a cuboid has a mass of 20kg and a volume of 0.4m3 and when placed on each face the pressures exerted are 400Pa, 250Pa and 500Pa. Take g=10m/s2 and work out the dimensions of the cuboid

Answer 1

Pressure is Force /Area

We know the pressure on each face.

We know the force, ie. the weight of the cuboid.

 

First, the weight of the cuboid = 20 kg *10 m/s² = 200 N

 

We can find the area of the first face by doing P=W/A -->   A = W/P = 200 N / 400 PA = .5 m²

The second area  -- > A = W/P = 200 N / 250 PA = .8 m²

Third area --> A = W/P = 200 N / 500 Pa = .4 m²

 

We need our 3 dimensions, L,D, W (length, depth, width) to multiply to .4m³

 

So L*D*W=.4 m³

We can randomly assign L,D,W to the faces above

 

So

1) L *W = .5m²

2) L*D = .8m²

3) W*D = .4 m²

 

Let's solve for some variables in terms of other variables:

 

L = .5/W  -->(using first equation of the three above)

.5/W * D = .8 --> D = .8 / (.5/W) = .8W/.5 = 1.6W  --> (plugging above equation into equation 2 above)

W*D = .4 -- >  W * 1.6W = .4

1.6W² = .4

W² = .4/1.6 = .25

W = .5

L = 1 m

D = .8 m² / L = .8/1 = .8   (Plugging L into equation 2 above to solve for D)

 

To make sure the volume is right, we can do L*W*D = 1*.5*.8 = .4

So the volume checks out, so your dimensions are 1 m, .8 m, and .5 m.