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 54 feet^2 of material to build the cube. What is the volume inside the giant sugar cube?

Answer 1

Answer: the volume is  27 ft^3

Step-by-step explanation:

We have that the surface of the cube is 54 ft^2

first, remember that a cube has 6 equal faces, this means that each face of the cube has a surface of:

f = (54/6) ft^2 = 9ft^2

each one of those faces has the same length in each side, and the surface of a square is equal to the length of one of the sides squared:

f = L^2 = 9ft^2

L = √( 9ft^2) = 3ft

now, the volume of a cube is equal to the cube of the length of the side:

v = L^3 = (3 ft)^3 = 27 ft^3

Answer 2

To find th volume, you must first use the surface are to find the dimension of one edge.

To do this, you take the total surface area of 54 ft.² and divided by six because there are six congruent faces. This will give us an area of 9 ft.² per face.

Because these are squares each dimension would need to be 3 feet.

To use this to find the volume multiply the length of 3 ft by the width of 3 ft by the height of 3ft.

The volume would be 27 cubic feet.