Question

Can anyone math experts help and guide me through these questions❓

question:
Given the volume, find the edge length of each cube.

Answer 1

A cube can be seen as a square that has been 'stretched'. We know that all four sides of a square are equal, thus, the sides of the faces of a cube are also equal.

In order to find the volume of a cube, the formula we apply is length x width x height (lwh).

Since all the sides are the same, another formula for the volume of the cube can be written as volume = x^3 in which x stands for the length of each side. When plugging in the formula:

1) V = 125 cm^3

125 = x^3

∛125 = x

5 = x

When finding the cube root, you can use a calculator or fingure out the answer yourself by multiplying any number by itself three times.

2) 8 = x^3

∛8 = x

2 = x

3) 343 = x^3

∛343 = x

7 = x

4) 1000 = x^3

∛1000 = x

10 = x

5) 1728 = x^3

∛1728 = x

12 = x

6) 1 = x^3

∛1 = x

1 = x

Make sure to include the appropriate unit for each answer

Answer 2

Explanation:

The volume of a cube is

`a {}^(3)`

where a is the side length,

Note: If you want to remember this formula, know that a cube is basically a bunch of squares stacked on one another vertically and horizontally

The area of a square with side length a, is

`{a}^(2)`

If we multiply that by the height of the cube, which is a.

`{a}^(2) * a = {a}^(3)`

That is the easy way to derive the formula of the volume of a cube.

Back on track, we know the volume so we must solve for a.

1.

`125 = {a}^(3)`

Assuming you took algebra, to isolate the variable a, we must undo it being raised to the third power.

To do this, we take the cube root of both sides

`\sqrt[3]{125} = \sqrt[3]{a {}^(3) }`

The cube root of 125 is 5 so

`5 = a`

5 cm

2.

`8 = {a}^(3)`

`\sqrt[3]{8} = \sqrt[3]{ {a}^(3) }`

`2 = a`

2 ft

3.

`343 = {a}^(3)`

`a = 7`

7 yd

4.

`1000 = a {}^(3)`

`10 = a`

10 mm

5.

`1728 = {a}^(3)`

`a = 12`

12 in. or 1 ft

6.

`1 = {a}^(3)`

`a = 1`

1 m