Question

How tall is a stack of cube shaped blocks whose volumes are 375 cube inches, 648 cube inches, and 1029 cube inches?

Answer 1

The stack of blocks is 25.96 inches tall

Explanation:

Volume of a Cube

Suppose we are given a cube of side L, the volume is calculated by:

`V=L^3`

If the volume is given, the side can be found by solving for L:

`L=\sqrt[3]{L}`

We know three cube-shaped blocks with volumes 375, 648, and 1029 cube inches. We'll find each of the side lengths and add them up to find the height that results when they stack up vertically.

Block 1, volume =375 cube inches:

`L_1=\sqrt[3]{375}=7.21\ inch`

Block 2, volume= 648 cube inches:

`L_2=\sqrt[3]{648}=8.65\ inch`

Block 3, volume =1029 cube inches:

`L_3=\sqrt[3]{1029}=10.10\ inch`

Total height=
`7.21\ inch+8.65\ inch+10.10\ inch=25.96\ inch`

The stack of blocks is 25.96 inches tall