Question

A storage company advertises two different choices for all your storage needs: "The Cube," a true cube with a volume of 64 m3 and "The Half" (half the volume of "The Cube"). What could be the dimensions of the two storage units?

Answer 1

Part 1) The dimensions of the storage " The Cube" are

`4\ m\ x\ 4\ m\ x\ 4\ m`

Part 2) The dimensions of the the storage " The Half" could be
`4\ m\ x\ 4\ m\ x\ 2\ m`

Explanation:

we know that

The volume of the cube is given by the formula

`V=b^3`

where

b is the length side of the cube

step 1

Find the dimensions of the storage " The Cube"

we have

`V=64\ m^3`

substitute in the formula of volume

`64=b^3`

solve for b

`b=\sqrt[3]{64}=4\ m`

therefore

The dimensions of the the storage " The Cube" are 4 m x 4 m x 4 m

step 2

Find the dimensions of the storage " The Half"

we have

`V=64/2=32\ m^3` ----> the volume is the half

Assume the shape of the storage " The Half" as a rectangular prism

The volume is equal to

`V=Bh`

where

B is the area of the base

h is the height of the storage

assume

`h=2\ m`

substitute in the formula of volume

`32=B(2)`

`B=16\ m^2`

If the base is a square the dimesnions of the base could be 4 m x 4 m

therefore

The dimensions of the the storage " The Half" could be
`4\ m\ x\ 4\ m\ x\ 2\ m`