Question

What is the new volume of a rectangular prism that is originally twelve cubic meters and is then resized using a scale factor of 3 on each side length?

four cubic meters

thirty-six cubic meters

one hundred eight cubic meters

three hundred twenty-four cubic meters

Answer 1

\(\bf
12=x\cdot x\cdot x=x^3\qquad {\color{red}{ 3}}x\cdot {\color{red}{ 3}}x\cdot {\color{red}{ 3}}x\implies {\color{red}{ 3^3}}x^3\\ \quad \\
x^3=12\qquad \qquad {\color{red}{ 3^3}}x^3={\color{red}{ 3^3}}\cdot 12\)