Question

I need to know how to find the volume of the smaller cube

Answer 1

Let's calculate the similarity scale:

`k=(2)/(5)`

The quotient of the volume of similar prism is equal to the cube of the similarity scale:

`(V_1)/(V_2)=k^3`

Substitute:

`k=(2)/(5),\ V_2=60\ cm^3\\\\(V_1)/(60)=\left((2)/(5)\right)^3\\\\(V_1)/(60)=(8)/(125)\ \ \ \ |\cdot60\\\\V_1=(8)/(125)\cdot60\\\\V_1=(8)/(25)\cdot12\\\\V_1=(96)/(25)\ cm^3\to V_1=3.84\ cm^3`