Question

B) A solid has volume defined by V = 4x3 – 12x²y + 9xy2. Identify the type of solid.

Answer 1

You can factor the formula for the volume as

$V = 4x^3-12x^2y+9xy^2 = x(2x-3y)^2$

So, your solid could be a prism. Its base is a square with side $2x-3y$ and height $x$.

So, its volume would be

$(2x-3y)\cdot (2x-3y) \cdot x = x(2x-3y)^2 = 4x^3-12x^2y+9xy^2$