Calculating Volume of a Cube using its Diagonal

In our previous discussion, we have seen how to calculate the volume of a cube using its side length. However, we can also use the diagonal of the cube to calculate its volume. This formula is quite simple and easy to understand.

The formula for calculating the volume of a cube using its diagonal (d) is given by:

Volume = √3/4 * d^3

where d is the length of the diagonal of the cube.

Let's take an example to illustrate this formula. Suppose we have a cube with side length 'a'. We can calculate the length of the diagonal (d) using the Pythagorean theorem, which states that:

d = √(a^2 + a^2 + a^2)

Simplifying this expression, we get:

d = √3 * a

Now, plugging in this value of d into the formula for volume, we get:

Volume = √3/4 * (√3 * a)^3

= (√3)^2 * a^3 / 4

= 1.5 * a^3

This is the same as the formula we derived earlier using the side length.

For instance, let's calculate the volume of a cube with side length k = 25 inches. Using the above formula, we get:

Volume = 1.5 * (25)^3

= 15625 cubic inches

Similarly, if we have a cube with side length k = 2 meters, its volume would be:

Volume = 1.5 * (2)^3

= 8 cubic meters

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In conclusion, calculating the volume of a cube using its diagonal is a simple process that can be done by plugging in the value of the diagonal into the formula. This formula is useful when we have the diagonal length of the cube and want to calculate its volume.

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