Answer:
The volume of fish tank is [tex]V = 2x^3+12x^2+22x+12[/tex]
Step-by-step explanation:
Area of base of fish tank is modeled by :
[tex]B(x)=2x^2 + 6x + 4[/tex]
Height of tank is modeled by equation :
[tex]H(x)=x+3[/tex]
Volume of fish tank =[tex]Base \times Height[/tex]
Volume of fish tank = [tex](2x^2+6x+4) \times (x+3)[/tex]
Volume of fish tank = [tex]x(2x^2+6x+4)+3(2x^2+6x+4)[/tex]
Volume of fish tank = [tex]2x^3+6x^2+4x+6x^2+18x+12[/tex]
Volume of fish tank [tex]V = 2x^3+12x^2+22x+12[/tex]
Hence The volume of fish tank is [tex]V = 2x^3+12x^2+22x+12[/tex]
