# 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?

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## 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?

The volume inside the giant sugar cube is 27 feet³

Step-by-step explanation:

* Lets explain how to solve the problem

– Cube has 6 square faces two bases and four side faces

– The surface area of the cube is the sum of areas of the six faces

– Area of a square with side length s square is s²

– The surface area of the cube is 6 s²

– The volume of the cube is s³

* Lets solve the problem

∵ A giant hollow sugar cube built out of wood

∵ It took 54 feet² of material to build the cube

∵ The surface area of the cube = 6 s²

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∴ 6 s² = 54 ⇒ divide both sides by 6

∴ s² = 9 ⇒ take √ for both sides

∴ s = √9 = 3

∴ The length of the side of the cube is 3 feet

∵ The volume of the cube = s³

∴ The volume of the cub = 3³ = 27

∴ The volume inside the giant sugar cube is 27 feet³

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