Question

The prism below is made of cubes which measure 3 of a centimeter on one side. What is the volume? NORSKEREN OA. LICO cubic cm OB. 8 cubic cm oc. i cubic cm 8 OD cubic cm 27

Answer 1

Recall that for a cube of this form

where the side is of length a, then the volume is calculated by the expression

`a^3`

So, to define the volume of the given cube, we should calculate the side's length of the bigger cube, based on the small cube

If we take a look at the front side of the cube we would look something like this

So, we want to determine the length's side of this square. We can see that in this case the length side corresponds to adding twice the length of one of the small cube. So the side's length of the new cube is

`(1)/(3)+(1)/(3)=(2)/(3)`

So, the volume of the bigger cube is

`((2)/(3))^3^{}=(2^3)/(3^3)=(8)/(27)`

So the volume of the bigger cube is 8/27 cubic centimeters