Question

BLOCKS Building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as 1/12x^2 centimeters, where x is the length of the packaging box. What is the volume of a building block in terms of x?

Answer 1

The volume of a cube is the product of its dimensions. Since all three dimensions have the same length, we just need to multiply the length of one dimension 3 times.

So if one dimension of the building block is equal 1/12x^2, we have that:

`\begin{gathered} \text{Volume}=d^3 \\ \text{Volume}=((1)/(12)x^2)^3 \\ \text{Volume}=((x^2)^3)/(12^3) \\ \text{Volume}=(x^6)/(1728) \end{gathered}`

So the volume of the building block is equal (1/1728)x^6.