Henry Ernest Dudeney/Modern Puzzles/96 - Concerning a Cube/Solution

by : $96$

 * Concerning a Cube

Solution

 * $(1): \quad$ $6$ feet


 * $(2): \quad$ Approximately $1 \cdotp 57$ feet


 * $(3): \quad$ $\dfrac 1 {36}$ feet

Proof
Let $l$ denote the length of the side of a cube $\CC$.

Let $\AA$ denote the superficial area of $\CC$.

Let $\VV$ denote the cubical contents of $\CC$.

From Surface Area of Cube:
 * $\AA = 6 l^2$

From Volume of Cube:
 * $\VV = l^3$

Hence we can deduce the following: