Question

How many cubic blocks with a side length of 1/6 cm are needed to fill the volume of this prism?

Answer 1

To answer this question we will compute the volume of the given rectangular prism, and the volume of a cube with a side of 1/6cm, and then we will divide the volume of the given prism by the volume of the cube.

The volume of the given rectangular prism is:

`V_p=(1)/(6)cm*(1)/(2)cm*(1)/(2)cm.`

Simplifying the above result we get:

`V_p=(1)/(24)cm^3.`

The volume of a cube with a side length of 1/6cm is:

`V_c=((1)/(6)cm)^3=(1)/(216)cm^3.`

Therefore we need

`(V_p)/(V_c)=((1)/(24)cm^3)/((1)/(216)cm^3)=(216)/(24)=9`

cubic blocks with a side length of 1/6cm in order to fill the volume of the given prism.

Answer: 9.