Question

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

A. V(x) = 2x^2 + 7x + 7

B. V(x) = 2x^2 + 5x + 1

C. V(x) = 2x^3 + 12x^2 + 22x + 12

D. V(x) = 2x^3 + 8x^2 + 10x + 4

Answer 1

C. V(x) = 2x^3 + 12x^2 + 22x + 12

Explanation:

The volume of a fish tank is the multiplication of the area of the base by the height.

In this question:

Area of the base:
`B(x) = 2x^(2) + 6x + 4`

Height:
`H(x) = x + 3`

Volume:

`V(x) = B(X)*H(x) = (2x^(2) + 6x + 4)(x + 3) = 2x^(3) + 6x^(2) + 4x + 6x^(2) + 18x + 12 = 2x^(3) + 12x^(2) + 22x + 12`

So the correct answer is:

C. V(x) = 2x^3 + 12x^2 + 22x + 12