Nicola said that 6 billion can represent the volume of a cube.How many units long is the cube?How do you know?

Question

Please help me! I cant figure it out because of the cube part! and please show how you go the answer! =]

Can you please explain how you got the Answer?

Answer 1

A cube is a shape that has 3 sides all of the same size ... IE the length is the same as the width which is also the same as the depth.
The volume of a cube is worked out by multiplying its L * W * D, but because they are the same length it is the same as saying L³ ( pronounced as, " L cubed")

So the volume of the cube is 6 billion, so;
6,000,000 = L³
therefore the cubed root of 6 billion is the side of the length
in math terms that is;
L = ³√(6,000,000)

Answer 2

A cube is a volume enclosed by six faces that are each a square of the same size.

Each edge of the cube is called a "side". All edges have the same length. Let us call this length "a"

The volume of the cube is a*a*a (a times a times a).

Because a is multiplied by itself a total of three times, it is often written a^3 (or a with a little 3 above and to the right: an exponent).

Because this is the way to calculate the volume of a cube, we call the operation of multiplying something by itself 3 times: taking the cube of the number.

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If you have the volume of the cube and you are trying to find the length of an edge, you are trying to find the number which, when multiplied by itself 3 times, will give the volume. We call this taking the cube root.

You are looking for a, such that a*a*a = 6 billion.

There are no easy way to do this by hand.

I assume you are using the "small" billion (the one used in the USA) 6,000,000,000

We know that a will be more than 1,000 because the cube of 1,000 is one billion (and we need 6)

We know that a will be less than 2,000, because the cube of 2,000 is the same as the cube of 2 times the cube of 1,000 = 2*2*2 times one billion = 8 billion (we only need 6).

Using a calculator, we find that the cube of 1.8171206 is very close to 6 (the real cube root of 6 is an irrational number, a number whose decimal expansion goes on forever).

So the cube root of 6 billion, the same as the cube root of 6 times the cube root of one billion = 1.8171206... times 1,000.

Approximately 1,817.12 (the number of units in the length of the cube)

Answer 3

A cube is basically a 3-d square. All of it's sides are equal.

The volume of a cube is Side 1 x Side 1 x Side 1.

So what you get is this: Volume = a^3

if a^3 = 6,000,000,000
A= 3rd root of 6 Billion
A= 1817.12

So the lenght of the cube is A which is 1817.12

Answer 4

Th formula is lwh. Since all of the sides of a cube are equal, this is basically reduced to s^3(the length of a side cubed).
S^3=6 x 10^9
s=cube root (6x10^9).
s=1817.1206

Answer 5

The volume of a cube = the length of a side of the cube, cubed, or taken to the third power.

So, if you know the volume of the cube, then the length of a side of the cube is = to the cube root of the volume.

(6,000,000,000)^1/3 = 1817.121

(1817.121)^3 = 6,000,000,000