Question

1.18. A fish tank has a base, B, with an area, in square inches, modeled by B(x) = 2x + 6x + 4.

Answer 1

Answer:

The volume of fish tank is $V(x)=2x^3+12x^2+22x+12$

Step-by-step explanation:

Area of Base of fish tank = $Length \times Breadth$

We are given that A fish tank has a base, B, with an area, in square inches, modeled by$B(x) = 2x^2 + 6x + 4.$

So,  $Length \times Breadth =2x^2 + 6x + 4.$

Height of tank = x+3

Volume of tank = $Length \times Breadth \times Height$

So, Volume of tank =$(2x^2 + 6x + 4)(x+3)$

Volume of Tank =$2x^3+6x^2+4x+6x^2+18x+12=2x^3+12x^2+22x+12$

Hence The volume of fish tank is $V(x)=2x^3+12x^2+22x+12$