Question

A farmer is building a grain silo storage. He estimates that will need 256 cubic yards of storage. The grain silo will be shaped as a cube. How long should one side of grain silo be?

Answer 1

When we refer to cube, this means than all sides have the same measures because its faces are square in shape.

Since area of a square is equal to the square of its sides, the volume of the cube it creates is equal to the cube of its sides.

Regular volume = length * width * height
Volume of a cube = side * side * side = (side)³

Given: Volume = 256 cubic yards.

We just need to get the cube root of the volume.

side = ∛256

Get the factors of 256 that has a whole number as its cube root and get the cube root.

side = ∛(8 * 32)
side = ∛8 * ∛32
side = 2 * ∛(8 * 4)
side = 2 * ∛8 * ∛4
side = 2 * 2 * ∛4
side = 4 ∛4

Each side of the cube will measure 4 ∛4 yards or 6.35 yards.

To check:

(4 ∛4)³ → 4³ * (∛4)³ → 64 * 4 = 256
6.35³ = 256.05

Answer 2

Having the length of a side(noticed with l), the volume of the cube is equal to:
V = l*l*l
V=l^3
To find the numeric value of l: l =
`\sqrt[3]{V}`

In our problem V = 256
l =
`\sqrt[3]{256} = \sqrt[3]{2^8} = 2^2\sqrt[3]{2^2} = 4 \sqrt[3]{4}`