Question

A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5 m2 of material to build the cube.

What is the volume inside the giant sugar cube?
Give an exact answer (do not round).

Answer 1

since: base=height=width, the width also equalssince: base=height=width, the width also equalsAnswer:

$\frac{27}{8} m^{3}$ or $3.375m^{3}$

Step-by-step explanation:

The formula for volume is Base * Height * Width; and the formula for area is Base * Height.

This problem mentions the structure is a cube and therefore it is assumed that every wall has the same area. Since there are 6 sides to a cube you divide the total amount of ft which make up this cube to know the area to each wall.

$13.5m/6=$ 2.25 or $\frac{9}{4}m$ per wall

With the area of each wall you can find the base and height:

base * height =  area

$b=\sqrt{\frac{9}{4} =\frac{3}{2} }$

base = $\frac{3}{2}$m

height = $\frac{3}{2}$m

since base = height = width, the width also equals $\frac{3}{2}$m

volume = $(\frac{3}{2})^{3} = \frac{27}{8}$