Question

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

The height, H, in inches, is modeled by HX) = x+3. Find the equation that models the fish tank's

volume, V, in cubic inches.

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

B. V(x) = 2x2 + 5x + 1

C. V(34) = 2x + 12x? +22x + 12

D.V(x) = 2x3 + 8x + 10x + 4

Answer 1

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

Explanation:

Area of Base of fish tank =
`Length * 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 * Breadth =2x^2 + 6x + 4.`

Height of tank = x+3

Volume of tank =
`Length * Breadth * 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`