153k views
3 votes
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?

1 Answer

2 votes

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

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

User Ulugbek
by
7.0k points