Answer:
The volume of fish tank is [tex]V(x)=2x^3+12x^2+22x+12[/tex]
Step-by-step explanation:
Area of Base of fish tank = [tex]Length \times Breadth[/tex]
We are given that A fish tank has a base, B, with an area, in square inches, modeled by[tex]B(x) = 2x^2 + 6x + 4.[/tex]
So, [tex]Length \times Breadth =2x^2 + 6x + 4.[/tex]
Height of tank = x+3
Volume of tank = [tex]Length \times Breadth \times Height[/tex]
So, Volume of tank =[tex](2x^2 + 6x + 4)(x+3)[/tex]
Volume of Tank =[tex]2x^3+6x^2+4x+6x^2+18x+12=2x^3+12x^2+22x+12[/tex]
Hence The volume of fish tank is [tex]V(x)=2x^3+12x^2+22x+12[/tex]
