# A cube has a surface area of 6534 square feet. What is its volume?

## let each side be x

we have 6 sides of area x^2

6x^2 = 6534
x^2 = 1089
x = √1089 = 33 ft

so volume = 33^3 ft^3 or 35937 ft^3

## Well, if a cube has a surface area of 6534 square feet, it's safe to say it's taking up quite a bit of space! As for the volume, let's take a closer look.

The surface area of a cube is given by the formula 6a^2, where 'a' represents the length of one side of the cube.

So, we can set up the equation 6a^2 = 6534 and solve for 'a'.

After dividing by 6, we have a^2 = 1089.

Now, taking the square root of both sides, we find that 'a' is equal to 33.

Since all sides of a cube have the same length, the volume of the cube is given by a^3.

Therefore, the volume of this cube would be 33^3 = 35937 cubic feet.

That's a whole lot of space to fill, so make sure you bring some giant-sized furniture to decorate it!

## To find the volume of a cube, we need to know the length of one side of the cube. However, the only information given is the surface area of the cube.

The formula to calculate the surface area of a cube is given by:

Surface Area = 6 * (side length)^2

Given that the surface area is 6534 square feet, we can set up the equation as follows:

6534 = 6 * (side length)^2

To solve for the side length, we can divide both sides of the equation by 6:

6534/6 = (side length)^2

Simplifying the equation:

1089 = (side length)^2

Now, we can take the square root of both sides to find the side length:

√1089 = side length

√1089 = 33

So, the length of one side of the cube is 33 feet.

To find the volume of the cube, we use the formula:

Volume = (side length)^3

Plugging in the value of the side length:

Volume = 33^3

Calculating:

Volume = 35937 cubic feet

Therefore, the volume of the cube is 35937 cubic feet.

## To find the volume of a cube, we need to know the length of its sides. Unfortunately, the given information is the surface area of the cube, not the length of its sides.

However, we can still solve this problem by finding the length of one side using the given surface area.

The formula to calculate the surface area of a cube is: Surface Area = 6 * (side length)^2

We can rearrange this formula to solve for the length of one side:
Side Length = sqrt(Surface Area / 6)

Plugging in the given surface area, we have:
Side Length = sqrt(6534 / 6)
Side Length = sqrt(1089)
Side Length = 33

Now that we know the length of one side is 33 feet, we can calculate the volume of the cube using the formula: Volume = (side length)^3

Plugging in the obtained side length, we have:
Volume = (33)^3
Volume = 35937 cubic feet

Therefore, the volume of the cube is 35937 cubic feet.