Question

A fish tank has a base, B, with an area, in square incheas, modeled by B(x) = 2x ^ 2 + 6x + 4. height, H , is modelod by H(x) = x + 3. Find the equation that models the fish tanks volume, V, in cubic inches.

Answer 1

The volume of fish tank is
`V = 2x^3+12x^2+22x+12`

Explanation:

Area of base of fish tank is modeled by :

`B(x)=2x^2 + 6x + 4`

Height of tank is modeled by equation :

`H(x)=x+3`

Volume of fish tank =
`Base * Height`

Volume of fish tank =
`(2x^2+6x+4) * (x+3)`

Volume of fish tank =
`x(2x^2+6x+4)+3(2x^2+6x+4)`

Volume of fish tank =
`2x^3+6x^2+4x+6x^2+18x+12`

Volume of fish tank
`V = 2x^3+12x^2+22x+12`

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