What is the length/width/height of a rectangle in metres, that's volume is 8,000 cubic feet?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

We know that the rectangular prism has length (l), width (w), and height (h)

We know that the volume (v) is:

 V = w*l*h

8000= w*l*h

Then we have multiple solutions since we do not know exactly the relation between the measurments:

For example:

l= 20 ft

w= 10 ft

h= 40 ft

==> V = 20*10*40 = 8000

Since we know that 1 m = 3 ft (approx.)

==> l= 20ft = 20/3 m= 6.6 m

==> w= 10 ft = 10/3 m= 3.3 m

==> h= 40 ft= 40/3 m = 13.3 m


krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

A rectangles is a four sided plane figure with four right angles. Please note that a rectangle, being a plane figure has no volume.

Perhaps the the term rectangle has been used in the question to mean a rectangular solid block.

The volume of a rectangular block is equal to the multiplication of its length, width and height. Thus:

Volume of a rectangular solid = Length x Width x Height

In the above formula if value of any 3 of the four variables are known the value of the fourth one can be calculated. However in the question only one of the four variables, that is volume is known. Therefore it is not possible to give unique values to the length, width and height.

Also please note that the volume is given in cubic feet while length, width and height are required to be calculated in meters. Therefor appropriate conversion of units of measurement will have to be done. We can calculate equivalent of any given volume in cubic feet in  meters by multiplying the figure in cubic feet with 0.0283168466.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The volume V of of the rectangular prism  is the product of length l, width w and height h and  is given by:

l*w*h = V.

l*w*h = 8000 c ft.

We can have many solutions. Some are as follows:

20'*20'*20' =8000c ft, if l=w=h = 20' =  20*0.3048 m =6.096 m, as  1 ft  = 0.3048meter.

For different length, width and heights , here are some solutions.

40'*20'*10' = 8000 c ft . So  l=  40 ft, w=20 ft, h = 10 ft. Or l,=40*0.3048 m = 1.192, W = 20*0.3048 = 6.096m and h = 3.048 m

50'* 20'*8 ' = 8000 cft. So l=50', w = 20' and h = 8' Orl = 15.24m wl= 15.24m, h = 2.4384

100 '* 10' * 8' = 8000 c ft. So, l=100, w = 10' and h= 8'. Or l = 30.48, w = 3.048m , h = 2.4384m.

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