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?

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Answer 1

Answer:

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

∴ 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

Answer 2

The volume inside the giant sugar cube which is built by A candy store called "Sugar" is 27 cubed feet.

What is the surface area of a cube?

Surface area of cube is the sum of the area of each face by which it is enclosed. The surface area of cube can be calculated with the following formula;

A=6a^2

Here, (a) is the length of side of the cube.

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 feet² of material to build the cube, which is equal to the surface area of cube as the sugar cube is hollow. Thus, the side of cube is,

$6a^2=54\\a^2=\dfrac{54}{6}\\a=\sqrt{9}\\a=3\rm\; ft$

The volume inside the giant sugar cube is equal to the cube of its side. Thus, the volume is,

$V=a^3\\V=3^3\\V=27\rm\; ft^3$

Hence, the volume inside the giant sugar cube which is built by A candy store called "Sugar" is 27 cubed feet.

Learn more about the surface area of the cube here;

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