# High School Math : Cubes

## Example Questions

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### Example Question #1 : How To Find The Length Of An Edge Of A Cube

Our backyard pool holds 10,000 gallons.  Its average depth is 4 feet deep and it is 10 feet long.  If there are 7.48 gallons in a cubic foot, how wide is the pool?

100 ft

30 ft

133 ft

33  ft

7.48 ft

33  ft

Explanation:

There are 7.48 gallons in cubic foot. Set up a ratio:

1 ft3 / 7.48 gallons = x cubic feet / 10,000 gallons

Pool Volume = 10,000 gallons = 10,000 gallons * (1 ft3/ 7.48 gallons) = 1336.9 ft3

Pool Volume = 4ft x 10 ft x WIDTH = 1336.9 cubic feet

Solve for WIDTH:

4 ft x 10 ft x WIDTH = 1336.9 cubic feet

WIDTH = 1336.9 / (4 x 10) = 33.4 ft

### Example Question #2 : How To Find The Length Of An Edge Of A Cube

A cube has a volume of 64cm3. What is the area of one side of the cube?

16cm2

16cm3

4cm2

16cm

4cm

16cm2

Explanation:

The cube has a volume of 64cm3, making the length of one edge 4cm (4 * 4 * 4 = 64).

So the area of one side is 4 * 4 = 16cm2

### Example Question #3 : How To Find The Length Of An Edge Of A Cube

Given that the suface area of a cube is 72, find the length of one of its sides.

Explanation:

The standard equation for surface area is

where  denotes side length. Rearrange the equation in terms of  to find the length of a side with the given surface area:

### Example Question #4 : How To Find The Length Of An Edge Of A Cube

Find the length of an edge of the following cube:

The volume of the cube is .

Explanation:

The formula for the volume of a cube is

,

where  is the length of the edge of a cube.

Plugging in our values, we get:

### Example Question #5 : How To Find The Length Of An Edge Of A Cube

Find the length of an edge of the following cube:

The volume of the cube is .

Explanation:

The formula for the volume of a cube is

,

where  is the length of the edge of a cube.

Plugging in our values, we get:

### Example Question #6 : How To Find The Length Of An Edge Of A Cube

What is the length of an edge of a cube that has a surface area of 54?

Explanation:

The surface area of a cube can be determined using the following equation:

### Example Question #1 : Cubes

Find the length of the diagonal connecting opposite corners of a cube with sides of length .

units

units

units

units

units

Explanation:

Find the diagonal of one face of the cube using the Pythagorean Theorem applied to a triangle formed by two sides of that face ( and ) and the diagonal itself ():

This diagonal is now the base of a new right triangle (call this ). The height of that triangle is an edge of the cube that runs perpendicular to this diagonal (call this ). The third side of the triangle formed by  and  is a line from one corner of the cube to the other, i.e., the cube's diagonal (call this ). Use the Pythagorean Theorem again with the triangle formed by , and  to find the length of this diagonal.

### Example Question #2 : Cubes

Find the length of the diagonal of the following cube:

Explanation:

To find the length of the diagonal, use the formula for a  triangle:

The length of the diagonal is .

### Example Question #1 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a side length of 15?

Explanation:

To find the surface area of a cube we must count the number of surface faces and add the areas of each of them together.

In a cube there are 6 faces, each a square with the same side lengths.

In this example the side lengths is 15 so the area of each square would be

We then multiply this number by 6, the number of faces of the cube, to get

Our answer for the surface area is .

### Example Question #2 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a side length of ?