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

Answer:

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 $4\ m\ x\ 4\ m\ x\ 2\ m$

Step-by-step 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 $4\ m\ x\ 4\ m\ x\ 2\ m$